Question

In the following figure, ABCD is a trapezium of area 24.5 cm² , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

Answer 1

Area of trapezium =\[\left( 3\pi + 2 \right) m^2\] 

\[\Rightarrow 24 . 5 = \frac{1}{2}\left( 10 + 4 \right) \times AB\]
\[ \Rightarrow AB = 3 . 5 cm\]

Area of shaded region = Area of trapezium ABCD − Area of quadrant ABE

\[= 24 . 5 - \frac{1}{4} \times \frac{22}{7} \times \left( 3 . 5 \right)^2 \]

\[ = 24 . 5 - 9 . 625\]

\[ = 14 . 875 {cm}^2\]

Hence, the area of shaded region is 14.875 cm²