Question

Quadrilateral ABCD is a trapezium of area 24.5 square centimetre side a d parallel side BC and angle dab is equal to 90 degree is equal to 10 cm and BC is equal to 4 cm if a b is a quadrant of a circle find the area of the shaded region is equal to 22 upon 7

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