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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.
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