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Question

An equilateral (ABC) is inscribed in a circle as shown. if the area of the circle is 36πcm², what exact area of the equilateral triangle A=πr².

 

Answer 1

Area of circle A = 36π cm²

Formula for area of circle = πr²

πr² = 36π

r² = 36

r = 6

Radius of circle(r) = 6 cm.

Area of an equilateral triangle = [(√3)a²]/4

Where a is side of equilateral triangle.

The side of an inscribed equilateral triangle is a = (√3)r

a = (√3)6

Substitute the value of a in (√3)a²/4.

Area of an equilateral triangle = [(√3)(6√3)²]/4

= [(√3(36*3)]/4

= 27√3

Area of an equilateral triangle = 27(√3)cm².