Question

the shape of a park is a rectangle with sides 40m and 35m bounded by semicircles attached to the sides measuring 35m, find the area and perimeter of the park.


Answer is : 2362.5 m², 190m​

Answer 1

Answer:

Given:

length = 40m

breadth = 35m

$Area_{rectangle} = 35 × 40 = 1400sqm$

Now there are 2 semi-circles each bounded to the two breadths.

If our breadth is 35m, our diameter of the semi-circle would be 35m as well.

So our radius (r) is 35/2 = 17.5 m

Find area of one semi circle:

$Area_{semi-circle} = \frac {3.14 \: × r^2}{2}$

So:

$Area_{semi-circle} = \frac {961.625}{2} \\ = 480.8125$

So, total area of 2 semi-circles is twice the area of this semi-circle, which is 961.63 sqm.

So, total area of the park

= 1400 + 961.63

= 2361.63 sqm

Perimeter will be:

$Perimeter =2l + 2b + (3.14 × 35) \\ = 150+109.9 \\ = 159.9m$

Hope this helped.