Question

A playground 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).

Answer 1

It is given that the playground is in the shape of a rectangle with two semicircles on its smaller sides.
Length of the rectangular portion is 36 m and its width is 24 . 5 m as shown in the figure below.

Thus, the area of the playground will be the sum of the area of a rectangle and the areas of the two semicircles with equal diameter 24 . 5 m.
Now, area of rectangle with length 36m and width 24 . 5m:
Area of rectangle = length x width
 = 36m x 24 . 5 m
\[ = 882 m^2 \]
Radius of the semicircle = r =\[ \frac{\text{ diameter }}{2} = \frac{24 . 5}{2} = 12 . 25m\]
∴ Area of the semicircle \[ = \frac{1}{2} \pi r^2 \]
\[ = \frac{1}{2} \times \frac{22}{7} \times (12 . 25 )^2 \]
\[ = 235 . 8 m^2 \]
∴ Area of the complete playground = area of the rectangular ground + 2 x area of a semicircle
\[ = 882 + 2 \times 235 . 8\]
\[ = 1353 . 6 m^2\]