# A play ground has the shape of a rectangle,

Question:

A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take π = 22.7).

Solution:

It is given that a play ground has a shape of rectangle, with two semicircles on its smaller sides as diameter, added to its outside. So,

Area of play ground $=$ Area of rectangle $+2 \times$ Area of semicircle

We have, sides of rectangle l = 36 m and b = 24.5 m.

Since, the diameter of semicircle is $2 r=b$. Then,

$r=\frac{24.5}{2}$

$=12.25 \mathrm{~m}$

Area of semicircle $=\frac{\pi r^{2}}{2}$

$=\frac{1}{2} \times \frac{22}{7} \times 12.25 \times 12.25$

$=235.81 \mathrm{~m}^{2}$

Area of rectangle $=l \times b$

$=36 \times 24.5$

$=882 \mathrm{~m}^{2}$

Thus, the area of playground is

Area of play ground $=$ Area of rectangle $+2 \times$ Area of semicircle

$=882+2 \times 235.81$

$=882+471.62$

$=1353.62 \mathrm{~m}^{2}$