What is the area of the circle inscribed in an equilateral triangle of side 12 cm?

A. \(6\pi\) cm²

B. \(12\pi\) cm²

C. \(36\pi\) cm²

D. \(48\pi\) cm²

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc cgl Save WhatsApp Report

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Answer: B. \(12\pi\) cm²

Answer: (B) \(12\pi\) cm²

Inradius of an equilateral triangle = \(\frac{a}{2\sqrt{3}} = \frac{12}{2\sqrt{3}} = 2\sqrt{3}\) cm.

Area = \(\pi (2\sqrt{3})^2 = 12\pi\) cm².

Trap: \(48\pi\) uses the circumradius \(\frac{a}{\sqrt{3}} = 4\sqrt{3}\).

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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