Mathematics Question and Solution
a² = √(8)
a = 2√(2) units.
a is the diameter of the orange half circle.
b = ½(a)
b = √(2) units.
b is the radius of the orange half circle.
Calculating c, radius of the inscribed purple circle.
2c+2-√(2) = √(2)
2c+2 = 2√(2)
c = (√(2)-1) units.
Therefore, Area Orange is;
Area half circle with radius √(2) units - Area quarter circle with radius 2 units + Area isosceles right-angled triangle with base and height 2 units respectively - Area circle with radius (√(2)-1) units.
= ½*π√(2)² - ¼*2²π + ½*2² - π(√(2)-1)²
= π-π+2-π(2-2√(2)+1)
= 2-3π+2√(2)π
= (2-(3-2√(2))π) square units.
= 1.46098791555 square units.
= 1.46 square units to 2 decimal places.
