Question

In the fig., ABC is a right-angled triangle, $\angle$ B = 90${}^o$, AB = 28 cm and BC = 21 cm. With AC as diameter, a semi-circle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region.

Answer 1

Given $\angle B={90}^{\circ },AB=28cm,BC=21cm$

Area of shaded region$=ar△ABC+$area of semicircle AC-ar quarter circle BC

$=\frac{1}{2}\times BC\times AB+\frac{1}{2}\times \pi {\left(\frac{AC}{2}\right)}^2-\frac{1}{4}\times \pi {\left(BC\right)}^2$

$=[\frac{1}{2}\times 21\times 28]+[\frac{1}{2}\times \frac{22}{7}\times \frac{1}{4}{\left(\sqrt{{28}^2+{21}^2}\right)}^2]-\frac{1}{4}\times \frac{22}{7}\times 21\times 21$

$=294+[\frac{11}{28}\times 1225]-346.5$

$=294+481.25-346.5=428.75㎠$