Question

Find the area of the shaded region if $\Delta ABC$ is an equilateral triangle of side 6 cm.

• A. 6.15 cm.
• B. 5.15 cm.
• C. 4 cm.
• D. 3.12 cm.

Answer 1

The correct option is A 6.15 cm.

$Height=AD=\frac{\sqrt{3}}{2}\times side=\frac{\sqrt{3}}{2}\times 6=3\sqrt{3}cm\therefore Inradius=\frac{1}{3}\times height=\frac{1}{3}\times 3\sqrt{3}=\sqrt{3}cm$
Area(shaded region) $=Area\left(\Delta ABC\right)-Area$ (incircle)
$=\frac{\sqrt{3}}{4}\times (side{)}^2-\pi r^2=\frac{\sqrt{3}}{4}\times 6\times 6-3.14\times (\sqrt{3}{)}^2$


= 15.57 - 9.42 = 6.15 cm