Question

Find the areas(in $c{m}^2$) of shaded regions. [Take $\pi =\frac{22}{7}$]

• A. $\frac{49}{2}$
• B. $\frac{35}{2}$
• C. $\frac{119}{4}$

Answer 1

First figure is a rectangle with a circle inscribed in it.
Area of the shaded region $=$ Area of the rectangle $-$ Area of the circle.
Area of the rectangle $=8\times 7=56c{m}^2$
Area of the circle $=\pi \times \frac{7}{2}\times \frac{7}{2}$
$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}=\frac{77}{2}c{m}^2$
$\Rightarrow$ Area of the shaded region $=56-\frac{77}{2}=\frac{35}{2}c{m}^2$

Second figure is a rectangle with four quarter circles inscribed in it.
Area of the shaded region $=$ Area of the rectangle - ($4\times$ Area of one quarter circle)
Area of rectangle $=9\times 7=63c{m}^2$
Area of four quarter circles $=4\times \frac{1}{4}\times \pi \times \frac{7}{2}\times \frac{7}{2}=\frac{77}{2}c{m}^2$
$\Rightarrow$ Area of the shaded region $=63-\frac{77}{2}=\frac{49}{2}c{m}^2$

Third figure is a square with a semicircle inscribed in it.
Area of the shaded region $=$ Area of the square $-$ Area of the semi-circle.
Area of the square $=7\times 7=49c{m}^2$
Area of the semi-circle $=\frac{1}{2}\times \pi \times \frac{7}{2}\times \frac{7}{2}=\frac{77}{4}c{m}^2$
$\Rightarrow$ Area of the shaded region $=49-\frac{77}{4}=\frac{119}{4}c{m}^2$