Mathematics Question and Solution
Let a be the radius of the half circle.
b² = (3√(3))²+a²
b = √(27+a²) units.
cosc = 3√(3)/√(27+a²) --- (1).
a² = 3²+(3√(3))²-2*3*3√(3)cosc
a² = 36+18√(3)cosc --- (2).
Substituting (1) in (2).
a² = 36+18√(3)(3√(3)/√(27+a²))
a² = 36+((162/√(27+a²))
a²-36 = (162/√(27+a²))
Therefore;
a = 3√(6) units.
Again, a is the radius of the semi circle.
It implies, area semi circle is;
½*πa²
= ½*π(3√(6))²
= ½(54)π
= 27π square units.
