Mathematics

Find the area of circle circumscribing an equilateral triangle of side 15 cm.

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Given,

Side of an equilateral triangle = 15 cm.

For an equilateral,

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

R = $\dfrac{15}{\sqrt{3}} = 5\sqrt{3}$ cm.

Area of circle = πR²

= $\pi(5\sqrt{3})^2$

= π × 25 × ( $\sqrt{3}$ )²

= π × 25 × 3

= 3.14 × 75 = 235.5 cm².

Hence, area of circle = 235.5 cm².

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