Question

abcd is trapezium of area 24.5 sq.cm.in it,AD||BC,angleDAB=90 degree ,AD=10cm and BC =4cm.if ABE is a quadrant of a circle,find the area of the shaded region.

Answer 1

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)
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
= 9.625 cm2

Area of the shaded region = Area of the trapezium - Area of the quadrant of the circle
= 24.5 - 9.625
= 14.875 cm2

Answer 2

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