Question

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm². The area of the triangle is ______.

Options

• 49 cm²

• `(49sqrt(3))/4` cm²

• `(7sqrt(3))/4` cm²

• 77 cm²

Answer 1

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm². The area of the triangle is `underlinebb((49sqrt(3))/4 cm^2)`.

Explanation:

Area of the circle = 154 cm².

∴ πR² = 154 cm²

⇒ `22/7 xx R^2 = 154  cm^2`

⇒ `R^2 = (154 xx 7/22) cm^2 = 7^2 cm^2`

⇒ R = 7 cm

∴ Side of the triangle = Radius of the circle = 7 cm.

Ares of the triangle = `(sqrt(3)/4 xx 7 xx 7) cm^2`

= `(49sqrt(3))/4 cm^2`