Correct Answer - Option 3 : 24.6 cm

2
**Given****∶**

An equilateral triangle with side 12 cm.

**Formula** **Used**∶

Area of an equilateral triangle = (√3/4) × side^{2}

Height of an equilateral triangle = (√ 3/2) × side

**Calculation** **∶**

When a circle is inscribed in an equilateral triangle, the radius of the circle will be 1/3 of the height of the triangle.

So, Height of an equilateral triangles = (√3/2) × side

h = √3/2 × 12 = 6√3 cm.

Now, Radius of the circle = 1/3 × height

⇒ r = 1/3 × 6√3 = 2√3 cm

Area of an equilateral triangle = √3/4 side^{2}

⇒ A = √3/4 × (12)^{2} = 36√3 cm^{2}

Now, Area of the circle = πr^{2}

⇒ a = π × (2√3)^{2}

⇒ a = 12 π cm^{2}

Area of the remaining portion of the triangle = A - a = 36√3 - 12π = 36 × 1.73 - 12 × 3.14 = 62.28 - 37.68 = 24.6 cm^{2}

**∴ The area of the remaining portion of the triangle is 24.6 cm**^{2}.