Mensuration Practice Test 3

Length of the wire = 132 cm
Side of the equilateral triangle = $\frac{132}{2}$ = 44 cm
Area of the equilateral triangle = $\frac{\sqrt{3}}{4}{\mathit{a}}^2$
= $\frac{\sqrt{3}}{4}\times 44\times 44$
= 580.8 $\mathit{c}{\mathit{m}}^2$
Side of the square = $\frac{132}{4}$ = 33 cm
Area of the square = 33 × 33 = 1,089 $\mathit{c}{\mathit{m}}^2$
Radius of the circle ⇒ 2πr = 132
r = $\frac{132\times 7}{22}\times \frac{1}{2}$ = 21 cm
Area of the circle = $\mathit{\pi }{\mathit{r}}^2$
= $\frac{22}{7}\times 21\times 21$ = $1386\mathit{c}{\mathit{m}}^2$
Side of regular hexagon = $\frac{132}{6}$ = 22 cm
Area of regular hexagon = $\frac{\sqrt{3}}{4}{\mathit{a}}^2\times 3$
= $\frac{\sqrt{3}}{4}$ × 22 × 22 × 3
= $\frac{1785.96}{4}$ = $446.49\mathit{c}{\mathit{m}}^2$
The area included is the largest when the shape is a circle.