Question

A playground in form of rectangle having semicircles on shorter sides .Find the area when length of the rectangular portion is 80 m and breadth is 42 m

Answer 1

Answer:

Let the length and breadth of the rectangular portion of the playground be l and b respectively. Then, l = 80m and b = 42 m.

Let r be the radius of each of the semicircular parts. Then r =

$\frac{b}{2} = \frac{42}{2} \: m = 21m$

Area of the playground = Area of rectangle + Area of 2 semicircles

$= (l \times b) + \: ( 2 \times \frac{\pi \: r {}^{2} }{2} ) = lb \: + \pi \: r {}^{2} \\ \\ = (80 \times 42 + \frac{22}{7} \times 21 \times 21) {m}^{2} \\ \ \\ \ (3360 + 1387) {m}^{2} \: = {4746m}^{2}$

✅ Hence the area of the playground is 4746m²

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