Question

Find the perimeter and area of the shaded portion.

Answer 1

The given figure is a combination of a rectangle ABCD and two semicircles AEB and DFC of equal area.
Given : Length of the rectangle, l $=4$ cm
Breadth of the rectangle, b $=2$ cm
Diameter of a semicircle $=2$ cm
$\therefore$ Radius of a semicircle, r = $\frac{2}{2}=1cm$
$\therefore$ Perimeter of the given figure $=AD+BC+\widehat{AEB}+\widehat{DFC}$
$=4+4+2\times \frac{1}{2}\times$ (circumference of a circle)
$=8+2\times \frac{1}{2}\times 2\pi r$
$=8+2\times \frac{22}{7}\times 1$
$=8+2\times 3.14$
$=8+6.28$
$\therefore$ Perimeter of the given figure = 14.28 cm
Area of the given figure = Area of a rectangle ABCD + 2 $\times$ Area of a semicircle
$=l\times b+2\times \frac{\pi r^2}{2}$
$=4\times 2+2\times \frac{22\times 1\times 1}{7\times 2}$
$\therefore$ Total area $=8+3.14=11.14$ cm${}^2$.