Question

Triangle ABC is an equilateral triangle and O is the center of its inscribed circle. If the area of the circle is 4π cm2, what is the area of triangle ABC?

Answer 1

Area of ABC = 16
`√(2)`

Explanation:

if Area of Circle is π·r², which in this case equals 4π, then the radius is 2; this gives us the height of the triangle as 4

since it's a 60-60-60 triangle, the height perpendicular to base creates a 30-60-90 triangle, whose sides are in the ratio of 1 : √2 : 2

therefore the entire base is 4√2 + 4√2 or 8√2

A (ΔABC) = 1/2(4) · 8√2 = 16√2

Answer 2

does one side of equilateral triangle is diameter. I will redo it.