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  4. A circle of radius 2 cm is inscribed in an equilateral triangle. Find the area of the triangle in cm 2.

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Q. A circle of radius $2 \,cm$ is inscribed in an equilateral triangle. Find the area of the triangle in $cm ^2$.

Mensuration

Solution:

(i) Radius of the circle is one-third of the median of the triangle.
(ii) Inradius is $2 cm$.
(iii) Height of the equilateral triangle $=3(2 cm )=$ $6 cm$.
(iv) Area of an equilateral triangle $=\frac{h^2}{\sqrt{3}}$.