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

In order to solve this sum you must know this formula:

Area of triangle AOC + Area of triangle BOC + Area of triangle AOB = Area of triangle ABC.

This formula will help you getting the value of radius. Once you get the value of radius you can simply subtract the area of circle from area of triangle to find the area of the shaded region.

Now, ( 0.5 × AC × OQ) + (0.5 × BC × OP) + (0.5 × AB × OR) = √3/4 × (side)²

or, AB = BC = Ac = 12.

or, 3 × 0.5 × 12 × radius = √3/4× 12²

or, radius = 3.46 cm.

We know area of triangle = √3/4×(12)² = 62.35 cm²

Also, area of circle = π(2√3)² = 37.71

∵Area of the portion of the triangle not included in the circle = 62.35 − 37.71 cm² = 24.64 cm². [Ans]

Answer 2

Answer:

Step-by-step explanation: