### Measurements Class 8th Mathematics Term 1 Tamilnadu Board Solution

##### Question 1.Find the perimeter of the following figures Answer:Perimeter = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4= 32 cmQuestion 2.Find the perimeter of the following figures Answer:Perimeter = 10 + 2 + 4 + 8 + 2 + 8 + 4 + 2= 40 cmQuestion 3.Find the perimeter of the following figures Answer:Radius of semi-circle = 4 cmPerimeter of semi-circle = πr= 3.14 × 4= 12.56 cmPerimeter of figure = 12.56 + 4 + 4 + (6-4) + 4 + 6= 30.56 cmQuestion 4.Find the perimeter of the following figures Answer:Perimeter = 7 + 13 + 13 + 7= 40 cmQuestion 5.Find the perimeter of the following figures Answer:Perimeter = 10 + 10 + 10 + 6 + 13 + 10 + 13 + 6 + 10 + 10= 98 cmQuestion 6.Find the area of the following figures Answer:Height of trapezium = 14-8= 6 cmArea 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 cm2Area of square = 8 × 8= 64 cm2Area of figure = Area of trapezium + Area of square= 60 + 64= 124 cm2Question 7.Find the area of the following figures Answer:The figure can be re-drawn as: Area of first triangle = 1/2 × base × height⇒ A1 = = 6 cm2Area of second triangle = 1/2 × base × height⇒ A2 = 4 cm2Area of rectangle = length × breadth⇒ A3 = 3 × 2= 6 cm2Area of square = (side)2⇒ A4 = 3 × 3= 9 cm2∴ Area of figure = A1 + A2 + A3 + A4= 6 + 4 + 6 + 9= 25 cm2Question 8.Find the area of the following figures Answer:Diameter of semicircle = 14cmRadius of semicircle = = 7 cm  = 77 cm2Area of square = (side)2 = 14 × 14= 196 cm2Area of figure = Area of semicircle + Area of square= 77 + 196= 273 cm2Question 9.Find the area of the following figures Answer:We know, Area of two quadrants  = 25.14 cm2Area of rectangle = length × breadth= 6 × 4= 24 cm2Question 10.Find the area of the following figures Answer:Radius of bigger semicircle = 2.1 mRadius of smaller semicircles = 1.05 mArea of 2 smaller semicircles ∴Area of 2 smaller semicircles = πr2Hence, area of 2 smaller semicircles = 1.7325 m2Area of bigger semicircle ∴Area of bigger semicircle = 6.93 m2Question 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 m2Area of smaller rectangle (shaded in grey) = length × breadth= 6 × 2= 12 m2Area of the coloured regions = Area of bigger rectangle + Area ofsmaller rectangleArea of the coloured regions = 16 + 12= 28 m2Question 12.Find the area of the coloured regions Answer:Area of rectangle = length × breadth= 16 × 20= 320 m2Area of square = side × side= 6 × 6= 36 m2Area of the coloured regions = Area of rectangle + Area of squareArea of the coloured regions = 320 + 36= 356 m2Question 13.Find the area of the coloured regions Answer:Radius of smaller semicircle = 7 cmRadius of bigger semicircle = 14 cmArea of smaller semicircle  = 77 cm2  = 308 cm2Area of the coloured regions = (Area of bigger semicircle-Area ofsmaller semicircle) + Area of smaller semicircleArea of the coloured regions = (308-77) + 77= 308 cm2Question 14.Find the area of the coloured regions Answer:Area of square = 7 × 7= 49 cm2Area of semicircle  = 19.25 cm2Area of coloured region = Area of square - 2 × Area of semicircle= 49-2 × 19.25= 49-38.5= 10.5 cm2Question 15.Find the area of the coloured regions Answer:Area of rectangle = 18 × 7= 126 cm2Radius of bigger semicircle = 3.5 cmArea of bigger semicircle  = 19.25 cm2Radius of smaller semicircle = 1.75 cmArea of unshaded region = πr2 = 9.625 cm2Area of coloured region = Area of bigger semicircle + ( Area ofRectangle- Area of unshaded region)Area of coloured region = 19.25 + (126-9.625)= 19.25 + 116.375= 135.625 cm2Question 16.Find the area of the coloured regions Answer:   = 9.625 cm2Area of triangle = 1/2 × base × height= 1/2 × 3.5 × 2= 3.5 cm2Area of coloured region = Area of quadrant - Area of triangle= 9.625-3.5= 6.125 cm2Question 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 cmBC = 10 cmAB = 54-10 = 44 cmRadius of bigger circle = = 27 cmArea of bigger circle = πr2 = 2291.14Radius of smaller circle = = 22 cmArea of smaller circle = πR2 = 1521.14Area of the shaded portion = Area of bigger circle- Area of smallerCircle= 2291.14-1521.14= 769.99 cm2= 770 cm2Question 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 m2  = 154 m2Therefore, Area of the field left ungrazed by the cow = 1440-154= 1286 m2Question 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 cmOne flower bed is a quadrant of the circle.We know, ⇒ Area of one flower bed = 3.14 × 14 × 14= 616 m2Area of the square park = 100 × 100= 10000 m2Area of the four-flower bed = 4 × 616= 2464 m2Thus area of the remaining part = (10000-2464) m2= 7536 m2Question 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 cm2Area of unshaded region = 4 × Area of 1 quadrant + Area of circle    = 6.28 cm2Therefore,Area of shaded region = Area of square- Area ofunshaded regionArea of shaded region = 16-6.28= 9.72 cm2Question 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 = 14cmRadius of semi–circle = 7cmArea of semi-circle  = 77 cm2Area of sheet = 20 × 14 = 280 cm2Thus, Area of remaining sheet = 280-77= 203 cm2Question 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 cmArea of square = (side)2= 42 × 42= 1764 cm2Area of each circle = πr2 = 154 cm2Area of 9 circles = 9 × 154= 1386 cm2Area of unshaded region = Area of square – Area of 9 circle= 1764 -1386= 378 cm2

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