Finding area of semi circle inscribed in an equilateral triangle.

[@steveduffy8726]

why is the distance at the top of the triangle = r ?

[@cowboyteacher5243]

This big triangle is the equilateral triangle. The angle made at the top of equilateral triangle is 60°. Therefore the angle made at the top of right angled triangle will be half of that i-e 30°. The other angle is 90°. Since we know that the sum of 3 angles in a triangle is 180°, therefore the angle formed at the center of circle will be 60°.
That's why the distance of hypotenuse in a right angled triangle will be twice of the distance of base 'r'