The perimeter of a sheet of paper in the shape of a quadrant of a circle is 75 cm. Its area would be $$\left( {\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

According to the figure,
⇒ Perimeter = r + r + $$l$$
⇒ 75 cm = 2r + length of arc
⇒ 75 cm = 2r + $$\frac{{2\pi r}}{4}$$
⇒ 75 cm = 2r + $$\frac{{22 \times r}}{{7 \times 2}}$$
⇒ r = 21 cm
⇒ Its area $$ = \frac{1}{4}\left[ {\frac{{22}}{7} \times 21 \times 21} \right] = 346.5{\text{ c}}{{\text{m}}^2}$$