Consider the semicircle sits on an isosceles triangle.

 is the area of the semicircle.

is the area of the triangle .

Consider the radius of the semicircle as .

In the right angle triangle, .

From the figure,

.

Area of the semicircle is .

Substitute  in the .

Area of the right angle triangle is .

Here base of the right angle triangle is radius of the semi circle.

Therefore .

In the right angle triangle, .

From the figure,

.

Thus and .

Area of the triangle , .

Substitute corresponding values in the above expression.

Determination of:

Substitute and in the above expression.

.

.