In an equilateral triangle of side 42 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is:
Answer & explanation
Correct answer: option 4
Area of triangle = \(\frac{\sqrt{3}}{4}\) a²
= \(\frac{\sqrt{3}}{4}\) x 42 x 42 = 441\(\sqrt {3}\) cm²
In - radius of ∆ = \(\frac{a}{2\sqrt{3}}\) = \(\frac{42}{2\sqrt{3}}\) = 7\(\sqrt {3}\)
Area of the circle = \(\pi \)r² = \(\frac{22}{7}\) x 7\(\sqrt {3}\) x 7\(\sqrt {3}\) = 462 cm²
Area of the remaining portion = 441\(\sqrt {3}\) - 462 = 21 [21\(\sqrt {3}\) - 22] cm²