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

Answer 1

$r=7cm$

Area of semi circle $=\frac{{\Pi r}^2}{2}=\frac{\Pi \times 7\times 7}{2}=\frac{49\Pi }{2}=76.969$

Perimeter of semicircle $=\Pi r+2\left(7\right)=\Pi \left(7\right)+14=7\Pi +14=\Pi i$

Perimeter of square $=4S=7\Pi +14$

$S=\frac{7(\Pi +2)}{4}$

Area of square $=S^2=\frac{49}{16}{(\Pi +2)}^2=80.9602$

$\therefore$ , Area of square $>$ Area of semicircle