Question

A piece of wire that has been bent in the form of a semicircle including the

bounding diameter is straightened and then bent in the form the of a square.

The diameter of the semicircle is 14 cm. Which has a larger area, the semi-

circle or the square? Also, find the difference between them.​

Answer 1

Step-by-step explanation:

$area \: of \: semicircle = \frac{\pi \: r ^{2} }{2} = \frac{22 \times 7 \times 7}{7 \times 2} = 77 {cm}^{2}$

$perimeter \: of \: semicircle = \frac{2\pi \: r}{2} + 14 \\ = \frac{2 \times 22 \times7}{7 \times 2} + 14 \\ = 22 + 14 = 36cm$

$perimeter \: of \: square = \frac{36}{4} = 9cm \\ area \: of \: square = {9}^{2} = 81 {cm}^{2}$

$square \: has \: large \: area \: than \: area \: of \: semicircle \: by \: 4{cm}^{2}$