Mathematics Question and Solution
Let a be the radius of the inscribed semi circle.
Therefore;
Calculating a.
(2a)²+a² = 25²
5a² = 25*25
a = 5√(5) units.
2a is;
2*5√(5)
= 10√(5) units.
Therefore, red shaded region is;
Area triangle with height 10√(5) units and base 5√(5) units - Area square with side 5√(5) units + Area quarter circle with radius 5√(5) units.
= ½*10√(5)*5√(5)-(5√(5))²+¼(5√(5))²π
= 125-125+¼(125π)
= ¼(125π) square units.
