Question

In Figure 3, OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region  ?\[[Use\pi = \frac{22}{7}]\]

Answer 1

Area of the quadrant OABC\[= \frac{1}{4} \times \pi r^2\]\[= \left( \frac{1}{4} \times \frac{22}{7} \times 7 \times 7 \right) {cm}^2 \]
\[ = \frac{77}{2} {cm}^2\]

Area of ΔODC\[=\]\[\frac{1}{2} \times OD \times OC\]

\[= \left( \frac{1}{2} \times 4 \times 7 \right) {cm}^2 ( \because \text{OC is the radius of the circle})\]

\[ = 14 {cm}^2\]

Area of the shaded region = Area of the quadrant OABC − Area of ΔODC

\[= \frac{77}{2} {cm}^2 - 14 {cm}^2 \]
\[ = \frac{77 - 28}{2} {cm}^2 \]
\[ = \frac{49}{2} {cm}^2 \]
\[ = 24 . 5 {cm}^2 \]