##### Class 8^{th} Mathematics Term 1 Tamilnadu Board Solution

**Exercise 2.1**- Area of a semicircle is ________ times the area of the circle. Choose the…
- Perimeter of a semicircle is ________ Choose the correct answer:A. (pi +2/2) r…
- If the radius of a circle is 7 m, then the area of the semicircle is _______…
- If the area of a circle is 144 cm^2 , then the area of its quadrant is _______…
- The perimeter of the quadrant of a circle of diameter 84 cm is _______ Choose…
- The number of quadrants in a circle is_______ Choose the correct answer:A. 1 B.…
- Quadrant of a circle is ______ of the circle. Choose the correct answer:A.…
- The central angle of a semicircle is _________ Choose the correct answer:A. 90°…
- The central angle of a quadrant is _______ Choose the correct answer:A. 90° B.…
- If the area of a semicircle is 84 cm^2 , then the area of the circle is _______…
- 35 cm Find the perimeter and area of semicircles whose radii are,…
- 10.5 cm Find the perimeter and area of semicircles whose radii are,…
- 6.3 m Find the perimeter and area of semicircles whose radii are,…
- 4.9 m Find the perimeter and area of semicircles whose radii are,…
- 2.8 cm Find the perimeter and area of semicircles whose diameters are,…
- 56 cm Find the perimeter and area of semicircles whose diameters are,…
- 84 cm Find the perimeter and area of semicircles whose diameters are,…
- 112 m Find the perimeter and area of semicircles whose diameters are,…
- 98 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
- 70 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
- 42 m Calculate the perimeter and area of a quadrant of the circles whose radii…
- 28 m Calculate the perimeter and area of a quadrant of the circles whose radii…
- Find the area of the semicircle ACB and the quadrant BOC in the given figure.…
- A park is in the shape of a semicircle with radius 21 m. Find the cost of…

**Exercise 2.2**- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the area of the following figures
- Find the area of the following figures
- a Find the area of the following figures
- Find the area of the following figures
- left arrow Find the area of the following figures
- Find the area of the coloured regions
- Find the area of the coloured regions
- 14cm/14cm Find the area of the coloured regions
- Find the area of the coloured regions
- a Find the area of the coloured regions
- s Find the area of the coloured regions
- In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10…
- A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36…
- A square park has each side of 100 m. At each corner of the park there is a…
- Find the area of the shaded region shown in the figure. The four corners are…
- A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A…
- On a square handkerchief, nine circular designs each of radius 7 cm are made.…

**Exercise 2.1**

- Area of a semicircle is ________ times the area of the circle. Choose the…
- Perimeter of a semicircle is ________ Choose the correct answer:A. (pi +2/2) r…
- If the radius of a circle is 7 m, then the area of the semicircle is _______…
- If the area of a circle is 144 cm^2 , then the area of its quadrant is _______…
- The perimeter of the quadrant of a circle of diameter 84 cm is _______ Choose…
- The number of quadrants in a circle is_______ Choose the correct answer:A. 1 B.…
- Quadrant of a circle is ______ of the circle. Choose the correct answer:A.…
- The central angle of a semicircle is _________ Choose the correct answer:A. 90°…
- The central angle of a quadrant is _______ Choose the correct answer:A. 90° B.…
- If the area of a semicircle is 84 cm^2 , then the area of the circle is _______…
- 35 cm Find the perimeter and area of semicircles whose radii are,…
- 10.5 cm Find the perimeter and area of semicircles whose radii are,…
- 6.3 m Find the perimeter and area of semicircles whose radii are,…
- 4.9 m Find the perimeter and area of semicircles whose radii are,…
- 2.8 cm Find the perimeter and area of semicircles whose diameters are,…
- 56 cm Find the perimeter and area of semicircles whose diameters are,…
- 84 cm Find the perimeter and area of semicircles whose diameters are,…
- 112 m Find the perimeter and area of semicircles whose diameters are,…
- 98 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
- 70 cm Calculate the perimeter and area of a quadrant of the circles whose radii…
- 42 m Calculate the perimeter and area of a quadrant of the circles whose radii…
- 28 m Calculate the perimeter and area of a quadrant of the circles whose radii…
- Find the area of the semicircle ACB and the quadrant BOC in the given figure.…
- A park is in the shape of a semicircle with radius 21 m. Find the cost of…

**Exercise 2.2**

- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the perimeter of the following figures
- Find the area of the following figures
- Find the area of the following figures
- a Find the area of the following figures
- Find the area of the following figures
- left arrow Find the area of the following figures
- Find the area of the coloured regions
- Find the area of the coloured regions
- 14cm/14cm Find the area of the coloured regions
- Find the area of the coloured regions
- a Find the area of the coloured regions
- s Find the area of the coloured regions
- In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10…
- A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36…
- A square park has each side of 100 m. At each corner of the park there is a…
- Find the area of the shaded region shown in the figure. The four corners are…
- A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A…
- On a square handkerchief, nine circular designs each of radius 7 cm are made.…

###### Exercise 2.1

**Question 1.**Choose the correct answer:

Area of a semicircle is ________ times the area of the circle.

A. two

B. four

C. one-half

D. one-quarter

**Answer:**As a semicircle is exact one-half of a full circle, the area of a semicircle is one-half times the area of the circle.

**Question 2.**Choose the correct answer:

Perimeter of a semicircle is ________

A.

B. (Ï€ + 2) r units

C. 2r units

D. (Ï€ + 4) r units

**Answer:**Perimeter of a full circle = 2Ï€r

Thus, Perimeter of a semicircle is

= Ï€r + 2r

= (Ï€ + 2)r units

**Question 3.**Choose the correct answer:

If the radius of a circle is 7 m, then the area of the semicircle is _______

A. 77 m^{2}

B. 44 m^{2}

C. 88 m^{2}

D. 154 m^{2}

**Answer:**Area of a semi-circle

= 77 m^{2}

**Question 4.**Choose the correct answer:

If the area of a circle is 144 cm^{2}, then the area of its quadrant is _______

A. 144 cm^{2}

B. 12 cm^{2}

C. 72 cm^{2}

D. 36 cm^{2}

**Answer:**Given, Area of a circle = 144 cm^{2}

Thus, area of its quadrant is

= 36 cm^{2}

**Question 5.**Choose the correct answer:

The perimeter of the quadrant of a circle of diameter 84 cm is _______

A. 150 cm

B. 120 cm

C. 21 cm

D. 42 cm

**Answer:**Given, Diameter = 84 cm

So, Radius =

= 42 cm

Perimeter of the quadrant of a circle =

= 66 + 84

= 150 cm

**Question 6.**Choose the correct answer:

The number of quadrants in a circle is_______

A. 1

B. 2

C. 3

D. 4

**Answer:**A quadrant is one-fourth of anything.

Hence, the number of quadrants in a circle is 4.

**Question 7.**Choose the correct answer:

Quadrant of a circle is ______ of the circle.

A. one-half

B. one-fourth

C. one-third

D. two-thirds

**Answer:**A quadrant of a circle is always one-fourth of the full circle .

Hence, Quadrant of a circle is one-fourth of the circle.

**Question 8.**Choose the correct answer:

The central angle of a semicircle is _________

A. 90°

B. 270°

C. 180°

D. 360°

**Answer:**The central angle of a semicircle is always 180°.

**Question 9.**Choose the correct answer:

The central angle of a quadrant is _______

A. 90°

B. 180°

C. 270°

D. 0°

**Answer:**The central angle of a quadrant is always 90°.

**Question 10.**Choose the correct answer:

If the area of a semicircle is 84 cm^{2}, then the area of the circle is _______

A. 144 cm^{2}

B. 42 cm^{2}

C. 168 cm^{2}

D. 288 cm^{2}

**Answer:**Area of a semicircle = 84 cm^{2}

Since a circle is twice of semi-circle,

Thus, Area of the circle = 2 × 84

= 168 cm^{2}

**Question 11.**Find the perimeter and area of semicircles whose radii are,

35 cm

**Answer:**We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 35 cm

Perimeter of semicircle = Ï€r + 2r

= 180 cm

Area of semicircle

= 1925 cm^{2}

**Question 12.**Find the perimeter and area of semicircles whose radii are,

10.5 cm

**Answer:**We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 10.5 cm

Perimeter of semicircle = Ï€r + 2r

= 54 cm

= 173.25 cm^{2}

**Question 13.**Find the perimeter and area of semicircles whose radii are,

6.3 m

**Answer:**We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 6.3 cm

Perimeter of semicircle = Ï€r + 2r

= 32.4 cm

= 62.37 cm^{2}

**Question 14.**Find the perimeter and area of semicircles whose radii are,

4.9 m

**Answer:**We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 4.9 cm

Perimeter of semicircle = Ï€r + 2r

= 25.2 cm

= 37.73 cm^{2}

**Question 15.**Find the perimeter and area of semicircles whose diameters are,

2.8 cm

**Answer:**

Diameter = 2.8 cm

= 1.4 cm

Perimeter of semicircle = Ï€r + 2r

= 28 cm

= 3.08 cm^{2}

**Question 16.**Find the perimeter and area of semicircles whose diameters are,

56 cm

**Answer:**

Diameter = 56 cm

= 28 cm

Perimeter of semicircle = Ï€r + 2r

= 144 cm

= 1232 cm^{2}

**Question 17.**Find the perimeter and area of semicircles whose diameters are,

84 cm

**Answer:**

Diameter = 84 cm

= 42 cm

Perimeter of semicircle = Ï€r + 2r

= 216 cm

= 2772 cm^{2}

**Question 18.**Find the perimeter and area of semicircles whose diameters are,

112 m

**Answer:**

Diameter = 112 cm

= 56 cm

Perimeter of semicircle = Ï€r + 2r

= 288 cm

= 288 cm^{2}

**Question 19.**Calculate the perimeter and area of a quadrant of the circles whose radii are,

98 cm

**Answer:**

Radius = 98 cm

= 50 cm

= 962.5 cm^{2}

**Question 20.**Calculate the perimeter and area of a quadrant of the circles whose radii are,

70 cm

**Answer:**

Radius = 70 cm

= 250 cm

= 3850 cm^{2}

**Question 21.**Calculate the perimeter and area of a quadrant of the circles whose radii are,

42 m

**Answer:**

Radius = 42 cm

= 150 cm

= 1386 cm^{2}

**Question 22.**Calculate the perimeter and area of a quadrant of the circles whose radii are,

28 m

**Answer:**

Radius = 28 cm

= 100 cm

= 616 cm^{2}

**Question 23.**Find the area of the semicircle ACB and the quadrant BOC in the given figure.

**Answer:**Radius = 7 cm

So,

Area of semicircle ACB

= 77 cm^{2}

Area of quadrant BOC

= 38.5 cm^{2}

**Question 24.**A park is in the shape of a semicircle with radius 21 m. Find the cost of fencing it at the cost of ` 5 per metre.

**Answer:**Given, radius = 21 m

Cost of fencing per metre = Rs.5 per metre

Perimeter of semicircle = Ï€r + 2r

= 108 cm

Thus, Cost of fencing per = 108 × 5

= 540 cm^{2}

**Question 1.**

Choose the correct answer:

Area of a semicircle is ________ times the area of the circle.

A. two

B. four

C. one-half

D. one-quarter

**Answer:**

As a semicircle is exact one-half of a full circle, the area of a semicircle is one-half times the area of the circle.

**Question 2.**

Choose the correct answer:

Perimeter of a semicircle is ________

A.

B. (Ï€ + 2) r units

C. 2r units

D. (Ï€ + 4) r units

**Answer:**

Perimeter of a full circle = 2Ï€r

Thus, Perimeter of a semicircle is

= Ï€r + 2r

= (Ï€ + 2)r units

**Question 3.**

Choose the correct answer:

If the radius of a circle is 7 m, then the area of the semicircle is _______

A. 77 m^{2}

B. 44 m^{2}

C. 88 m^{2}

D. 154 m^{2}

**Answer:**

Area of a semi-circle

= 77 m^{2}

**Question 4.**

Choose the correct answer:

If the area of a circle is 144 cm^{2}, then the area of its quadrant is _______

A. 144 cm^{2}

B. 12 cm^{2}

C. 72 cm^{2}

D. 36 cm^{2}

**Answer:**

Given, Area of a circle = 144 cm^{2}

Thus, area of its quadrant is

= 36 cm^{2}

**Question 5.**

Choose the correct answer:

The perimeter of the quadrant of a circle of diameter 84 cm is _______

A. 150 cm

B. 120 cm

C. 21 cm

D. 42 cm

**Answer:**

Given, Diameter = 84 cm

So, Radius =

= 42 cm

Perimeter of the quadrant of a circle =

= 66 + 84

= 150 cm

**Question 6.**

Choose the correct answer:

The number of quadrants in a circle is_______

A. 1

B. 2

C. 3

D. 4

**Answer:**

A quadrant is one-fourth of anything.

Hence, the number of quadrants in a circle is 4.

**Question 7.**

Choose the correct answer:

Quadrant of a circle is ______ of the circle.

A. one-half

B. one-fourth

C. one-third

D. two-thirds

**Answer:**

A quadrant of a circle is always one-fourth of the full circle .

Hence, Quadrant of a circle is one-fourth of the circle.

**Question 8.**

Choose the correct answer:

The central angle of a semicircle is _________

A. 90°

B. 270°

C. 180°

D. 360°

**Answer:**

The central angle of a semicircle is always 180°.

**Question 9.**

Choose the correct answer:

The central angle of a quadrant is _______

A. 90°

B. 180°

C. 270°

D. 0°

**Answer:**

The central angle of a quadrant is always 90°.

**Question 10.**

Choose the correct answer:

If the area of a semicircle is 84 cm^{2}, then the area of the circle is _______

A. 144 cm^{2}

B. 42 cm^{2}

C. 168 cm^{2}

D. 288 cm^{2}

**Answer:**

Area of a semicircle = 84 cm^{2}

Since a circle is twice of semi-circle,

Thus, Area of the circle = 2 × 84

= 168 cm^{2}

**Question 11.**

Find the perimeter and area of semicircles whose radii are,

35 cm

**Answer:**

We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 35 cm

Perimeter of semicircle = Ï€r + 2r

= 180 cm

Area of semicircle

= 1925 cm^{2}

**Question 12.**

Find the perimeter and area of semicircles whose radii are,

10.5 cm

**Answer:**

We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 10.5 cm

Perimeter of semicircle = Ï€r + 2r

= 54 cm

= 173.25 cm^{2}

**Question 13.**

Find the perimeter and area of semicircles whose radii are,

6.3 m

**Answer:**

We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 6.3 cm

Perimeter of semicircle = Ï€r + 2r

= 32.4 cm

= 62.37 cm^{2}

**Question 14.**

Find the perimeter and area of semicircles whose radii are,

4.9 m

**Answer:**

We know, Perimeter of semicircle = Ï€r + 2r

And,

Area of semicircle

Radius = 4.9 cm

Perimeter of semicircle = Ï€r + 2r

= 25.2 cm

= 37.73 cm^{2}

**Question 15.**

Find the perimeter and area of semicircles whose diameters are,

2.8 cm

**Answer:**

Diameter = 2.8 cm

= 1.4 cm

Perimeter of semicircle = Ï€r + 2r

= 28 cm

= 3.08 cm^{2}

**Question 16.**

Find the perimeter and area of semicircles whose diameters are,

56 cm

**Answer:**

Diameter = 56 cm

= 28 cm

Perimeter of semicircle = Ï€r + 2r

= 144 cm

= 1232 cm^{2}

**Question 17.**

Find the perimeter and area of semicircles whose diameters are,

84 cm

**Answer:**

Diameter = 84 cm

= 42 cm

Perimeter of semicircle = Ï€r + 2r

= 216 cm

= 2772 cm^{2}

**Question 18.**

Find the perimeter and area of semicircles whose diameters are,

112 m

**Answer:**

Diameter = 112 cm

= 56 cm

Perimeter of semicircle = Ï€r + 2r

= 288 cm

= 288 cm^{2}

**Question 19.**

Calculate the perimeter and area of a quadrant of the circles whose radii are,

98 cm

**Answer:**

Radius = 98 cm

= 50 cm

= 962.5 cm^{2}

**Question 20.**

Calculate the perimeter and area of a quadrant of the circles whose radii are,

70 cm

**Answer:**

Radius = 70 cm

= 250 cm

= 3850 cm^{2}

**Question 21.**

Calculate the perimeter and area of a quadrant of the circles whose radii are,

42 m

**Answer:**

Radius = 42 cm

= 150 cm

= 1386 cm^{2}

**Question 22.**

Calculate the perimeter and area of a quadrant of the circles whose radii are,

28 m

**Answer:**

Radius = 28 cm

= 100 cm

= 616 cm^{2}

**Question 23.**

Find the area of the semicircle ACB and the quadrant BOC in the given figure.

**Answer:**

Radius = 7 cm

So,

Area of semicircle ACB

= 77 cm^{2}

Area of quadrant BOC

= 38.5 cm^{2}

**Question 24.**

A park is in the shape of a semicircle with radius 21 m. Find the cost of fencing it at the cost of ` 5 per metre.

**Answer:**

Given, radius = 21 m

Cost of fencing per metre = Rs.5 per metre

Perimeter of semicircle = Ï€r + 2r

= 108 cm

Thus, Cost of fencing per = 108 × 5

= 540 cm^{2}

###### Exercise 2.2

**Question 1.**Find the perimeter of the following figures

**Answer:**Perimeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4

= 32 cm

**Question 2.**Find the perimeter of the following figures

**Answer:**Perimeter = 10 + 2 + 4 + 8 + 2 + 8 + 4 + 2

= 40 cm

**Question 3.**Find the perimeter of the following figures

**Answer:**Radius of semi-circle = 4 cm

Perimeter of semi-circle = Ï€r

= 3.14 × 4

= 12.56 cm

Perimeter of figure = 12.56 + 4 + 4 + (6-4) + 4 + 6

= 30.56 cm

**Question 4.**Find the perimeter of the following figures

**Answer:**Perimeter = 7 + 13 + 13 + 7

= 40 cm

**Question 5.**Find the perimeter of the following figures

**Answer:**Perimeter = 10 + 10 + 10 + 6 + 13 + 10 + 13 + 6 + 10 + 10

= 98 cm

**Question 6.**Find the area of the following figures

**Answer:**Height of trapezium = 14-8

= 6 cm

Area of trapezium is given as, A = 1/2 × (a + b)h,

As shown below:

Where, a is the shorter side.

B is the longer side.

H is the distance between the two sides.

⇒ Area of trapezium

= 60 cm^{2}

Area of square = 8 × 8

= 64 cm^{2}

Area of figure = Area of trapezium + Area of square

= 60 + 64

= 124 cm^{2}

**Question 7.**Find the area of the following figures

**Answer:**The figure can be re-drawn as:

Area of first triangle = 1/2 × base × height

⇒ A_{1} =

= 6 cm^{2}

Area of second triangle = 1/2 × base × height

⇒ A_{2}

= 4 cm^{2}

Area of rectangle = length × breadth

⇒ A_{3} = 3 × 2

= 6 cm^{2}

Area of square = (side)^{2}

⇒ A_{4} = 3 × 3

= 9 cm^{2}

∴ Area of figure = A_{1} + A_{2} + A_{3} + A_{4}

= 6 + 4 + 6 + 9

= 25 cm^{2}

**Question 8.**Find the area of the following figures

**Answer:**Diameter of semicircle = 14cm

Radius of semicircle =

= 7 cm

= 77 cm^{2}

Area of square = (side)^{2} = 14 × 14

= 196 cm^{2}

Area of figure = Area of semicircle + Area of square

= 77 + 196

= 273 cm^{2}

**Question 9.**Find the area of the following figures

**Answer:**We know,

Area of two quadrants

= 25.14 cm^{2}

Area of rectangle = length × breadth

= 6 × 4

= 24 cm^{2}

**Question 10.**Find the area of the following figures

**Answer:**Radius of bigger semicircle = 2.1 m

Radius of smaller semicircles

= 1.05 m

Area of 2 smaller semicircles

∴Area of 2 smaller semicircles = Ï€r^{2}

Hence, area of 2 smaller semicircles

= 1.7325 m^{2}

Area of bigger semicircle

∴Area of bigger semicircle

= 6.93 m^{2}

**Question 11.**Find the area of the coloured regions

**Answer:**The figure is given below:

Area of bigger rectangle (shaded in green) = length × breadth

= 8 × 2

= 16 m^{2}

Area of smaller rectangle (shaded in grey) = length × breadth

= 6 × 2

= 12 m^{2}

Area of the coloured regions = Area of bigger rectangle + Area of

smaller rectangle

Area of the coloured regions = 16 + 12

= 28 m^{2}

**Question 12.**Find the area of the coloured regions

**Answer:**Area of rectangle = length × breadth

= 16 × 20

= 320 m^{2}

Area of square = side × side

= 6 × 6

= 36 m^{2}

Area of the coloured regions = Area of rectangle + Area of square

Area of the coloured regions = 320 + 36

= 356 m^{2}

**Question 13.**Find the area of the coloured regions

**Answer:**Radius of smaller semicircle

= 7 cm

Radius of bigger semicircle = 14 cm

Area of smaller semicircle

= 77 cm^{2}

= 308 cm^{2}

Area of the coloured regions = (Area of bigger semicircle-Area of

smaller semicircle) + Area of smaller semicircle

Area of the coloured regions = (308-77) + 77

= 308 cm^{2}

**Question 14.**Find the area of the coloured regions

**Answer:**Area of square = 7 × 7

= 49 cm^{2}

Area of semicircle

= 19.25 cm^{2}

Area of coloured region = Area of square - 2 × Area of semicircle

= 49-2 × 19.25

= 49-38.5

= 10.5 cm^{2}

**Question 15.**Find the area of the coloured regions

**Answer:**Area of rectangle = 18 × 7

= 126 cm^{2}

Radius of bigger semicircle = 3.5 cm

Area of bigger semicircle

= 19.25 cm^{2}

Radius of smaller semicircle

= 1.75 cm

Area of unshaded region = Ï€r^{2}

= 9.625 cm^{2}

Area of coloured region = Area of bigger semicircle + ( Area of

Rectangle- Area of unshaded region)

Area of coloured region = 19.25 + (126-9.625)

= 19.25 + 116.375

= 135.625 cm^{2}

**Question 16.**Find the area of the coloured regions

**Answer:**

= 9.625 cm^{2}

Area of triangle = 1/2 × base × height

= 1/2 × 3.5 × 2

= 3.5 cm^{2}

Area of coloured region = Area of quadrant - Area of triangle

= 9.625-3.5

= 6.125 cm^{2}

**Question 17.**In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10 cm, and O is the centre of bigger circle.

**Answer:**Given, AC = 54 cm

BC = 10 cm

AB = 54-10 = 44 cm

Radius of bigger circle =

= 27 cm

Area of bigger circle = Ï€r^{2}

= 2291.14

Radius of smaller circle =

= 22 cm

Area of smaller circle = Ï€R^{2}

= 1521.14

Area of the shaded portion = Area of bigger circle- Area of smaller

Circle

= 2291.14-1521.14

= 769.99 cm^{2}

= 770 cm^{2}

**Question 18.**A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36 m in one corner of the field by a rope of length 14 m. Find the area of the field left ungrazed by the cow.

**Answer:**The figure is shown below:

Area of rectangular field = 40 × 36

= 1440 m^{2}

= 154 m^{2}

Therefore, Area of the field left ungrazed by the cow = 1440-154

= 1286 m^{2}

**Question 19.**A square park has each side of 100 m. At each corner of the park there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure. Find the area of the remaining portion of the park.

**Answer:**Radius = 14 cm

One flower bed is a quadrant of the circle.

We know,

⇒ Area of one flower bed = 3.14 × 14 × 14

= 616 m^{2}

Area of the square park = 100 × 100

= 10000 m^{2}

Area of the four-flower bed = 4 × 616

= 2464 m^{2}

Thus area of the remaining part = (10000-2464) m^{2}

= 7536 m^{2}

**Question 20.**Find the area of the shaded region shown in the figure. The four corners are quadrants. At the center, there is a circle of diameter 2 cm.

**Answer:**Area of square = side × side

= 4 × 4

= 16 cm^{2}

Area of unshaded region = 4 × Area of 1 quadrant + Area of circle

= 6.28 cm^{2}

Therefore,

Area of shaded region = Area of square- Area of

unshaded region

Area of shaded region = 16-6.28

= 9.72 cm^{2}

**Question 21.**A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semicircular portion with BC as diameter is cut off. Find the area of the remaining part.

**Answer:**The figure is given below:

Diameter of semi-circle = BC = 14cm

Radius of semi–circle

= 7cm

Area of semi-circle

= 77 cm^{2}

Area of sheet = 20 × 14 = 280 cm^{2}

Thus, Area of remaining sheet = 280-77

= 203 cm^{2}

**Question 22.**On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of the remaining portion of the handkerchief.

**Answer:**From the figure,

Hence, it can be observed that size of side of square = 14 + 14 + 14 = 42 cm

Area of square = (side)^{2}

= 42 × 42

= 1764 cm^{2}

Area of each circle = Ï€r^{2}

= 154 cm^{2}

Area of 9 circles = 9 × 154

= 1386 cm^{2}

Area of unshaded region = Area of square – Area of 9 circle

= 1764 -1386

= 378 cm^{2}

**Question 1.**

Find the perimeter of the following figures

**Answer:**

Perimeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4

= 32 cm

**Question 2.**

Find the perimeter of the following figures

**Answer:**

Perimeter = 10 + 2 + 4 + 8 + 2 + 8 + 4 + 2

= 40 cm

**Question 3.**

Find the perimeter of the following figures

**Answer:**

Radius of semi-circle = 4 cm

Perimeter of semi-circle = Ï€r

= 3.14 × 4

= 12.56 cm

Perimeter of figure = 12.56 + 4 + 4 + (6-4) + 4 + 6

= 30.56 cm

**Question 4.**

Find the perimeter of the following figures

**Answer:**

Perimeter = 7 + 13 + 13 + 7

= 40 cm

**Question 5.**

Find the perimeter of the following figures

**Answer:**

Perimeter = 10 + 10 + 10 + 6 + 13 + 10 + 13 + 6 + 10 + 10

= 98 cm

**Question 6.**

Find the area of the following figures

**Answer:**

Height of trapezium = 14-8

= 6 cm

Area of trapezium is given as, A = 1/2 × (a + b)h,

As shown below:

Where, a is the shorter side.

B is the longer side.

H is the distance between the two sides.

⇒ Area of trapezium

= 60 cm^{2}

Area of square = 8 × 8

= 64 cm^{2}

Area of figure = Area of trapezium + Area of square

= 60 + 64

= 124 cm^{2}

**Question 7.**

Find the area of the following figures

**Answer:**

The figure can be re-drawn as:

Area of first triangle = 1/2 × base × height

⇒ A_{1} =

= 6 cm^{2}

Area of second triangle = 1/2 × base × height

⇒ A_{2}

= 4 cm^{2}

Area of rectangle = length × breadth

⇒ A_{3} = 3 × 2

= 6 cm^{2}

Area of square = (side)^{2}

⇒ A_{4} = 3 × 3

= 9 cm^{2}

∴ Area of figure = A_{1} + A_{2} + A_{3} + A_{4}

= 6 + 4 + 6 + 9

= 25 cm^{2}

**Question 8.**

Find the area of the following figures

**Answer:**

Diameter of semicircle = 14cm

Radius of semicircle =

= 7 cm

= 77 cm^{2}

Area of square = (side)^{2} = 14 × 14

= 196 cm^{2}

Area of figure = Area of semicircle + Area of square

= 77 + 196

= 273 cm^{2}

**Question 9.**

Find the area of the following figures

**Answer:**

We know,

Area of two quadrants

= 25.14 cm^{2}

Area of rectangle = length × breadth

= 6 × 4

= 24 cm^{2}

**Question 10.**

Find the area of the following figures

**Answer:**

Radius of bigger semicircle = 2.1 m

Radius of smaller semicircles

= 1.05 m

Area of 2 smaller semicircles

∴Area of 2 smaller semicircles = Ï€r^{2}

Hence, area of 2 smaller semicircles

= 1.7325 m^{2}

Area of bigger semicircle

∴Area of bigger semicircle

= 6.93 m^{2}

**Question 11.**

Find the area of the coloured regions

**Answer:**

The figure is given below:

Area of bigger rectangle (shaded in green) = length × breadth

= 8 × 2

= 16 m^{2}

Area of smaller rectangle (shaded in grey) = length × breadth

= 6 × 2

= 12 m^{2}

Area of the coloured regions = Area of bigger rectangle + Area of

smaller rectangle

Area of the coloured regions = 16 + 12

= 28 m^{2}

**Question 12.**

Find the area of the coloured regions

**Answer:**

Area of rectangle = length × breadth

= 16 × 20

= 320 m^{2}

Area of square = side × side

= 6 × 6

= 36 m^{2}

Area of the coloured regions = Area of rectangle + Area of square

Area of the coloured regions = 320 + 36

= 356 m^{2}

**Question 13.**

Find the area of the coloured regions

**Answer:**

Radius of smaller semicircle

= 7 cm

Radius of bigger semicircle = 14 cm

Area of smaller semicircle

= 77 cm^{2}

= 308 cm^{2}

Area of the coloured regions = (Area of bigger semicircle-Area of

smaller semicircle) + Area of smaller semicircle

Area of the coloured regions = (308-77) + 77

= 308 cm^{2}

**Question 14.**

Find the area of the coloured regions

**Answer:**

Area of square = 7 × 7

= 49 cm^{2}

Area of semicircle

= 19.25 cm^{2}

Area of coloured region = Area of square - 2 × Area of semicircle

= 49-2 × 19.25

= 49-38.5

= 10.5 cm^{2}

**Question 15.**

Find the area of the coloured regions

**Answer:**

Area of rectangle = 18 × 7

= 126 cm^{2}

Radius of bigger semicircle = 3.5 cm

Area of bigger semicircle

= 19.25 cm^{2}

Radius of smaller semicircle

= 1.75 cm

Area of unshaded region = Ï€r^{2}

= 9.625 cm^{2}

Area of coloured region = Area of bigger semicircle + ( Area of

Rectangle- Area of unshaded region)

Area of coloured region = 19.25 + (126-9.625)

= 19.25 + 116.375

= 135.625 cm^{2}

**Question 16.**

Find the area of the coloured regions

**Answer:**

= 9.625 cm^{2}

Area of triangle = 1/2 × base × height

= 1/2 × 3.5 × 2

= 3.5 cm^{2}

Area of coloured region = Area of quadrant - Area of triangle

= 9.625-3.5

= 6.125 cm^{2}

**Question 17.**

In the given figure, find the area of the shaded portion if AC = 54 cm, BC = 10 cm, and O is the centre of bigger circle.

**Answer:**

Given, AC = 54 cm

BC = 10 cm

AB = 54-10 = 44 cm

Radius of bigger circle =

= 27 cm

Area of bigger circle = Ï€r^{2}

= 2291.14

Radius of smaller circle =

= 22 cm

Area of smaller circle = Ï€R^{2}

= 1521.14

Area of the shaded portion = Area of bigger circle- Area of smaller

Circle

= 2291.14-1521.14

= 769.99 cm^{2}

= 770 cm^{2}

**Question 18.**

A cow is tied up for grazing inside a rectangular field of dimensions 40 m × 36 m in one corner of the field by a rope of length 14 m. Find the area of the field left ungrazed by the cow.

**Answer:**

The figure is shown below:

Area of rectangular field = 40 × 36

= 1440 m^{2}

= 154 m^{2}

Therefore, Area of the field left ungrazed by the cow = 1440-154

= 1286 m^{2}

**Question 19.**

A square park has each side of 100 m. At each corner of the park there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure. Find the area of the remaining portion of the park.

**Answer:**

Radius = 14 cm

One flower bed is a quadrant of the circle.

We know,

⇒ Area of one flower bed = 3.14 × 14 × 14

= 616 m^{2}

Area of the square park = 100 × 100

= 10000 m^{2}

Area of the four-flower bed = 4 × 616

= 2464 m^{2}

Thus area of the remaining part = (10000-2464) m^{2}

= 7536 m^{2}

**Question 20.**

Find the area of the shaded region shown in the figure. The four corners are quadrants. At the center, there is a circle of diameter 2 cm.

**Answer:**

Area of square = side × side

= 4 × 4

= 16 cm^{2}

Area of unshaded region = 4 × Area of 1 quadrant + Area of circle

= 6.28 cm^{2}

Therefore,

Area of shaded region = Area of square- Area of

unshaded region

Area of shaded region = 16-6.28

= 9.72 cm^{2}

**Question 21.**

A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semicircular portion with BC as diameter is cut off. Find the area of the remaining part.

**Answer:**

The figure is given below:

Diameter of semi-circle = BC = 14cm

Radius of semi–circle

= 7cm

Area of semi-circle

= 77 cm^{2}

Area of sheet = 20 × 14 = 280 cm^{2}

Thus, Area of remaining sheet = 280-77

= 203 cm^{2}

**Question 22.**

On a square handkerchief, nine circular designs each of radius 7 cm are made. Find the area of the remaining portion of the handkerchief.

**Answer:**

From the figure,

Hence, it can be observed that size of side of square = 14 + 14 + 14 = 42 cm

Area of square = (side)^{2}

= 42 × 42

= 1764 cm^{2}

Area of each circle = Ï€r^{2}

= 154 cm^{2}

Area of 9 circles = 9 × 154

= 1386 cm^{2}

Area of unshaded region = Area of square – Area of 9 circle

= 1764 -1386

= 378 cm^{2}