Question:
A circle is inscribed in an equilateral triangle of side 12 cm. What is the area of the circle?
12 सेमी भुजा वाले एक समबाहु त्रिभुज के अंतर्वृत्त का क्षेत्रफल क्या है?
Options:
- \(12\pi\) cm\(^2\)
- \(16\pi\) cm\(^2\)
- \(9\pi\) cm\(^2\)
- \(24\pi\) cm\(^2\)
- \(12\pi\) सेमी\(^2\)
- \(16\pi\) सेमी\(^2\)
- \(9\pi\) सेमी\(^2\)
- \(24\pi\) सेमी\(^2\)
Correct Answer: a)
Explanation:
Inradius of an equilateral triangle of side \(a\) is \(r = \frac{a}{2\sqrt{3}} = \frac{12}{2\sqrt{3}} = \frac{6}{\sqrt{3}} = 2\sqrt{3}\) cm.
Area of circle = \(\pi r^2 = \pi (2\sqrt{3})^2 = \pi (12) = 12\pi\) cm\(^2\).
Area of circle = \(\pi r^2 = \pi (2\sqrt{3})^2 = \pi (12) = 12\pi\) cm\(^2\).
अंतःत्रिज्या \(r = \frac{a}{2\sqrt{3}} = 2\sqrt{3}\) सेमी। क्षेत्रफल = \(\pi (2\sqrt{3})^2 = 12\pi\) सेमी\(^2\)।