Mathematics Question and Solution
Calculating Shaded Fraction.
Let the radius of the inscribed circle be 1 unit.
Therefore, the radius of the inscribed half circle is 2 units.
a² = 2²+(2+2)²
a² = 20
a = 2√(5) units.
a is the radius of the ascribed quarter circle.
Shaded Area is;
½*π(2)²+π(1)²
= 2π+π
= 3π square units.
Area ascribed quarter circle is;
¼*π(2√(5))²
= ¼(20π)
= 5π square units.
Therefore, shaded fraction area is;
Shaded Area ÷ Area ascribed quarter circle
= 3π÷5π
= ⅗
