Multiple choice

A circle of radius $4$ cm is inscribed in an equilateral triangle T. Find the area of T (in cm$\displaystyle ^{2}$)

  1. $\displaystyle 42\sqrt{3}$
  2. $\displaystyle 45\sqrt{3}$
  3. $\displaystyle 48\sqrt{3}$
  4. $\displaystyle 50\sqrt{3}$
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C Correct answer
Explanation

For an equilateral triangle, the inradius r = side / (2 * sqrt(3)). Given r=4, side = 8 * sqrt(3). Area = (sqrt(3)/4) * side^2 = (sqrt(3)/4) * (64 * 3) = 48 * sqrt(3).

AI explanation

The area of an equilateral triangle can be expressed in terms of its inradius r as 3*sqrt(3)r^2. Substituting the given radius of 4 cm into this formula yields an area of 3*sqrt(3)(4)^2. This calculates to 3*sqrt(3)*16, which equals 48*sqrt(3) square cm.

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