Question

In given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (Use $\pi =22/7$)

Answer 1

In right $△AED$, using Pythagoras theorem,

${AD}^2={AE}^2+{DE}^2=9^2+{12}^2=81+144=225cm$

$\Rightarrow AD=\sqrt{225}=15cm=diameter$

Required area = ar. ABCD + ar. semi-circle - ar $△AED=(20\times 15)+\frac{1}{2}\times \frac{22}{7}\times {\left(\frac{15}{2}\right)}^2-\frac{1}{2}\times 9\times 12$

$=300+88.3928-54=334.3928{cm}^2$