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) × side2
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 side2
⇒ A = √3/4 × (12)2 = 36√3 cm2
Now, Area of the circle = πr2
⇒ a = π × (2√3)2
⇒ a = 12 π cm2
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 cm2
∴ The area of the remaining portion of the triangle is 24.6 cm2.