Multiple choice

Find the area of a circle inscribed in an equilateral triangle of side $18 cm$. [Take $\pi \, =\, 3.14$]

  1. $84.78$ $cm^2$
  2. $85.78$ $cm^2$
  3. $86.78$ $cm^2$
  4. $87.78 $ $cm^2$
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A Correct answer
Explanation

For an equilateral triangle with side 'a', the inradius r = a / (2 * sqrt(3)). Here a = 18, so r = 18 / (2 * sqrt(3)) = 9 / sqrt(3) = 3 * sqrt(3). Area = pi * r^2 = 3.14 * (3 * sqrt(3))^2 = 3.14 * 27 = 84.78 cm^2.

AI explanation

The radius of a circle inscribed in an equilateral triangle is given by the formula r = a / (2 * sqrt(3)), where a is the side of the triangle. Substituting the side length gives r = 18 / (2 * sqrt(3)) = 9 / sqrt(3) = 3 * sqrt(3) cm. The area of the circle is pi * r^2, so using pi = 3.14, the area is 3.14 * (3 * sqrt(3))^2 = 3.14 * 27 = 84.78 sq cm.

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