Question

Find the area of the shaded design in Fig where $ABCD$ is a square of side $10cm$ and semicircles are drawn with each side of the square as diameter. (Use $\pi =3.14$)

Answer 1

Given:

Side of square $ABCD=10$cm

Area of square $ABCD={\left(side\right)}^2={10}^2=100sq.cm$

Given semicircle is drawn with side of square as diameter.

So, Diameter of semicircle $=$ Side of square $=10cm$

Radius of semicircle $=\frac{side}{2}=\frac{10}{2}=5cm$

$\begin{array}{cc}\text{Area of semi-circle}AD& =\frac{1}{2}\times \text{Area of circle}\\ & =\frac{1}{2}\times \pi r^2\\ & =\frac{1}{2}\times 3.14\times 5^2\\ & =\frac{3.14\times 25}{2}c{m}^2\end{array}$

Since radius is same for semi-circle $AD,BC,AB,CD$.

Area of semi circle $AD=$ Area of semi-circle $BC=$ Area of semicircle $AB=$ Area of semicircle $CD=\frac{3.14\times 25}{2}c{m}^2$

$\because \text{Area of}4\text{Semicircle}-\text{Area of shaded region}=\text{Area of square}ABCD$

$\begin{array}{cc}⟹\text{Area of shaded region}& =\text{Area of}4\text{Semicircle}-\text{Area of square}ABCD\\ & =(4\times \frac{3.14\times 25}{2})-100\\ & =\left(\frac{3.14\times 100}{2}\right)-100\\ & =\frac{314}{2}-100\\ & =157-100\\ & =57{cm}^2\end{array}$

Therefore, the area of shaded region is $57c{m}^2$.