Question

□ABCD is a trapezium of area 24.5 sq cm . side AD||side BC, angle DAB = 90 AD=10 cm &BC=4 cm . If ABE is a quadrant of a cricle . find the area of the shaded region (22/7)

Answer 1

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$<b>Que:-) ABCD is a trapezium of area 24.5 sq cm . side AD||side BC, angle DAB = 90 AD=10 cm &BC=4 cm . If ABE is a quadrant of a cricle . find the area of the shaded region (22/7)</b>$

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$\huge\sf{\blue{\star{\underline{Answer}}\star}}$

$<i>$

Area of the trapezium = h/2 (a + b)
where a and b are the parallel sides

h = perpendicular distance between the parallel sides

Area of the trapezium ABCD = AB/2 (AD + BC)

24.5 = (AB/2) (10 + 4)

49 = AB (14)

⏩$\boxed{\green{ AB = 3.5 cm}}$

Radius of the quadrant of the circle = AB = 3.5 cm

Area of the quadrant of the circle = 1/4πr²

= 1/4 x 22/7 x 3.5 x 3.5

⏩ $\boxed{\blue{9.625 cm^2}}$

$<b>Area of the shaded region</b>$

= Area of the trapezium - Area of the quadrant of the circle

= 24.5 - 9.625

⏩ $\boxed{\boxed{\large{\orange{14.875 cm^2}}}}$

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