Question

The figure consists of 3 semicircles and an equilateral triangle of side 7 cm. Find the area of the entire figure.

• A. 252.19$c{m}^2$
• B. 253.25 $c{m}^2$
• C. 134.75$c{m}^2$
• D. 78.94$c{m}^2$

Answer 1

The correct option is D

78.94$c{m}^2$

The figure can be simplified into an equilateral triangle and 3 semi-circular figures.

The area of the equilateral triangle is = $\frac{\left(\sqrt{3}{a}^2\right)}{4}$

=$\frac{(\sqrt{3}\times 7^2)}{4}$

The area of the semicircle = $\frac{1}{2}\times \pi \times r^2$ (r = $\frac{a}{2}$)

=$\frac{1}{2}\times \frac{22}{7}\times {3.5}^2$

The combined area of the figure = area of the triangle + 3 x (area of the semicircle)

=$\frac{(\sqrt{3}\times 7^2)}{4}$ + 3 $\times$ $\frac{1}{2}\times \frac{22}{7}\times {3.5}^2$

= 78.94 $c{m}^2$

The combined area of the figure is 78.94 $c{m}^2$