Multiple choice

In an equilateral triangle of side $24cm$, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle [Take $\sqrt 3=1.732$]

  1. $68.21cm^2$
  2. $98.55cm^2$
  3. $112.67cm^2$
  4. $154.12cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of an equilateral triangle is (sqrt(3)/4) * side^2 = (1.732/4) * 24^2 = 249.408 cm^2. The radius of the inscribed circle is side / (2 * sqrt(3)) = 24 / (2 * 1.732) = 6.928 cm, so the area of the circle is pi * r^2 = 3.14159 * 6.928^2 = 150.77 cm^2. The remaining area is 249.408 - 150.77 = 98.638 cm^2, which is closest to 98.55 cm^2.

AI explanation

The area of the equilateral triangle is found using the formula (root 3 divided by 4) multiplied by the square of the side, giving 249.408 square cm. The inradius is the area divided by the semi-perimeter, which equals 4, so the inscribed circle area is 16 multiplied by pi, or approximately 50.24 square cm. Subtracting this circle area from the total triangle area leaves a remaining portion of 98.55 square cm.

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