Question

In fig. is a trapezium of area $24.5{cm}^2$ ,In it , AD||BC,$\angle DAB={90}^0$, AC=10 cm and BC=4 cm.If ABE is a quadrant of a circle, the area of the shaded region.

Answer 1

$AC=10cmBC=4cm\angle DAB={90}^{\circ }AD||BC⟹\angle ABC={90}^{\circ }⟹A{C}^2=A{B}^2+B{C}^{2}100=A{B}^2+16A{B}^2=84$

Area of sector $AEB$ is given as

$\frac{90}{360}\times \pi A{B}^2=21\times \frac{22}{7}=66c{m}^2$

The area of shaded region is $245-66=179c{m}^2$