Question

a circle inscribed in a equilateral triangle of side 12cm. find the radius of inscribed circle and the area of the shaded region

Answer 1

Answer for your question....

Answer 2

Answer: 1) The radius of circle is 2√3 cm

2) The area of the shaded region is 24.64 cm²

Step-by-step explanation:

Given side of equilateral triangle = 12 cm

The radius of the circle inscribed in a equilateral triangle is given by

$r=\dfrac{a}{2\sqrt{3} }$ where a is side of equilateral triangle

$r= \dfrac{12}{2\sqrt{3} } =\dfrac{6}{\sqrt{3} } = \dfrac{6\sqrt{3} }{3} =2\sqrt{3} cm$

Now shaded area = ar. of triangle - ar of circle

$\dfrac{\sqrt{3} a^2}{4} - \pi r^2\\\\\Rightarrow \dfrac{\sqrt{3} (12)^2}{4} - \dfrac{22}{7} \times (2\sqrt{3} )^2\\\\\Rightarrow 36\sqrt{3} - 37.71\\\\\Rightarrow 62.35-37.71= 24.64cm^2$

Hence, the area of the shaded region is 24.64 cm² and the radius of circle is 2√3 cm