A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (the following figure). Find the radius of the inscribed circle and the area of the shaded part.

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Solution

We have to find the area of the shaded portion. We havewhich is an equilateral triangle and.

We have O as the incentre and OP, OQ and OR are equal.

So,

Thus,

So area of the shaded region,

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Similar questions

A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (Fig). Find the radius of the inscribed circle and the area of the shaded part.

Q. A circle is inscribed in an equilateral triangle ABC with side

12

cm, touching its sides. Find the radius of the inscribed circle and the area of the shaded part.

A circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region.
[Use $π = 3.14 a n d \sqrt{3} = 1.73$ ]