Question

A rectangle encloses four circles. The radius of each circle is $7cm$. Calculate the area of (a) the rectangle and (b) the shaded portion

Answer 1

Given

Radius of enclosed four circles $=7cm$

Diameter of a circle $=14cm$

Length of rectangle $=4\left(14\right)=56cm$ [As four circles cover the length of rectangle ]

Width of rectangle $=14cm$ [As only one circle covers width of rectangle]

(a) Area of rectangle $=$ Length $\times$ Width

$=56\times 14=784c{m}^2$

(b) Area of enclosed circle $=\pi r^2$

$=\frac{22}{7}\times 7\times 7$

$=154c{m}^2$

Area of enclosed four circles $=4\times 156=616c{m}^2$

$\therefore$ Area of shaded part $=784-616=168c{m}^2$