Question

an equilateral triangle inscribed in a circle with an area equal 578.67 cm square. Find the area of triangle

Answer 1

Answer:

Area of triangle ≈ 239.28 cm²

Step-by-step explanation:

Equilateral triangle height = radius + half radius = 1.5r

Let s be side of equilateral triangle.

Cutting triangle in half makes a right angle triangle with height h = 1.5r, hypotenuse = s and base b = 0.5s.

Using Pythagoras' Theorem:

(0.5s)² + (1.5r)² = s²

=> 0.25s² + 2.25r² = s²

=> 0.75s² = 2.25r²

=> s² = 3r²

=> s = √3 r

The base of the equilateral triangle is its side length s.

Area of triangle = 1/2 × base × height

= 1/2 × s × 1.5r

= 1/2 × √3r × 1.5r

≈ 1.29904 r²

Area of circle = π r² = 578.67 cm²

=> r² = 578.67 / π cm² ≈ 184.196 cm²

So

Area of triangle ≈ 1.29904 × 184.196 cm²

≈ 239.28 cm²