Mathematics Question and Solution
Let BC be 1 unit.
Therefore;
AB = 2 unit.
Radius of the circle, r is;
r = √(5) unit.
Therefore;
Area R is;
Area sector with radius √(5) unit and angle (2asin(√(2)/(2√(5))))° - 2(area triangle with height 1 unit and base (√(2)sin135) unit.
(2asin(√(2)/(2√(5))))*(√(5))²*π÷360) - 2(½*1*√(2)*sin135)
= (πasin(√(2)/(2√(5)))/36 - 1
= ((πasin(√(2)/(2√(5))) - 36)/36
= 0.60875277198 square unit.
Area square is;
2²
= 4 square unit.
It implies;
Area R ÷ Area Square as a single fraction is;
(((πasin(√(2)/(2√(5))) - 36)/36) ÷ 4
= ((πasin(√(2)/(2√(5))) - 36)/144
In its decimal form;
Area R ÷ Area Square is;
0.60875277198 ÷ 4
= 0.152188193
