Question

A circle is inscribed in an equilateral triangle of side 24 centimetre, touching its sides. What is the area of the remaining portion of the triangle in square centimetre?​

Answer 1

Refer formula for equilateral triangle

Radius of the circle inscribed

$⟹ \frac{24}{2 \sqrt{3} } = \frac{12}{ \sqrt{3} } {cm}^{2}$

Area of the circle inscribed

$\: ⟹ \: π( \frac{12}{ \sqrt{3} } {)}^{2} = \frac{144π}{3} = 48π {cm}^{2}$

Area of the equilateral triangle

$⟹144 \sqrt{3} - 48π {cm}^{2}$

Area of the remaining portion of the triangle

= area of the equilateral triangle - area of inscribed circle

$⟹144 \sqrt{3} - 48π {cm}^{2}$

Answer 2

Answer:

Hope Helps!!~

Refer attachment!!