# Tilak draw a triangular design. The triangle he drawn is equilateral with side 12 cm and then with the help of bangle he draw a circle inscribed in i

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Tilak draw a triangular design. The triangle  he drawn is equilateral with side 12 cm and then with the help of bangle he draw a circle inscribed in it touching its sides. Calculate the remaining area of triangle which is untouched by a circle.
1. 20.4 cm2
2. 26.4 cm2
3. 24.6 cm2
4. 22.6 cm2

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Correct Answer - Option 3 : 24.6 cm2

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.