Mathematics Question and Solution
Let the AC = AB = a (diameter of the semi circle).
Therefore;
sin22.5 = AD/AC
AD = asin22.5 units.
cos22.5 =CD/AC
CD = acos22.5 units.
Calculating a.
84+25+½(acos22.5)(asin22.5) = ½(a²)
109+⅛√(2)a² = ½(a²)
109 = ½(a²)-⅛√(2)a²
109 = ⅛(4-√(2))a²
872 = (4-√(2))a²
a = √(872/(4-√(2)))
a = 18.36377300632 units.
It implies;
Green Area is;
0.5a²-84-25
= 0.5*18.36377300632²-84-25
= 59.61407951382 square units.
Or
= 0.5*18.36377300632²*sin22.5*cos22.5
= 59.61407951388 square units.
