alleryA circle is inscribed in an equilateral triangle of side 12 cm. The area of the region between the triangle and the circle is approximately
A50 sq cm
B15 sq cm
C32 sq cm
D25.04 sq cm
Answer & Solution
Correct answer: D. 25.04 sq cm
1. Triangle area = (square root of 3)/4 × 144 ≈ 62.35 sq cm.
2. Incircle radius = side/(2 (square root of 3)) ≈ 3.464; area ≈ pi × 12 ≈ 37.71 (incircle).
3. Difference ≈ 62.35 - 37.71 ≈ 24.64 → option ≈ 25 sq cm.
_Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_
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