Mathematics

Find the area of a circle inscribed in an equilateral triangle of side 18 cm.

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For an equilateral triangle,

Radius of incircle = $\dfrac{\text{Length of each side of triangle}}{2\sqrt{3}}$

$= \dfrac{18}{2\sqrt{3}} \\[1em] = \dfrac{9}{\sqrt{3}} \\[1em] = 3\sqrt{3} \text{ cm}.$

Area of circle = πr²

= $3.14 \times (3\sqrt{3})^2$

= 3.14 × 27

= 84.78 cm².

Hence, area of circle = 84.78 cm².

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