Question

In an equilateral triangle of side 12cm, a circle is inscribed touching its sides. find the area of the portion of the triangle not included in the circle

Answer 1

your answer is 24.5 square cm bro

Answer 2

Answer:

Area is 24.74 square centimeter.

Step-by-step explanation:

Given the side of equilateral triangle which the circle is inscribed touching its sides. we have to find the area of the portion of the triangle not included in the circle.

$\text{Area of triangle=}\frac{\sqrt3}{4}a^2=\frac{\sqrt3}{4}(12)^2=62.35cm^2$

As radius is on the tangent perpendicularly bisect the tangent of circle ⇒ A'B=6 cm.

Now, we have to find the radius of circle in order to find the area of circle.

In the figure,

$tan30=\frac{OA'}{A'B}=\farc{OA'}{6}$

⇒ $OA'=\frac{6}{\sqrt3}=2\sqrt3cm$

$\text{Area of circle=}\pi r^2=\frac{22}{7}(2\sqrt3)^2=37.61cm^2$

Area of the portion of the triangle not included in the circle=62.35-37.61=24.74 square centimeter.