Mathematics Question and Solution
Calculating the area of the semi circle.
Let r be the radius of the half circle.
a = 2r units.
a is the diameter of the half circle.
b² = (2r)²+7²-2*7*2rcosx
b² = 4r²+49-28rcosx --- (1).
b² = 2(15)²+2(15)²cosx
b² = 450+450cosx --- (2).
cosx = 7/(2r) --- (3).
Calculating r.
Equating (1) and (2).
4r²+49-28rcosx = 450+450cosx
4r²-28rcosx = 401+450cosx --- (4).
Substituting (3) in (4).
4r²-28r(7/(2r)) = 401+450(7/(2r))
4r²-98 = 401+(1575/r)
4r² = 499+(1575/r)
4r³-499r = 1575
Observing trial and error approach.
r = 12.5 units.
r = ½(25) units.
Again, r is the radius of the ascribed half circle.
It implies, area half circle is;
½*r²*π
= ½*(½(25))²π
= ⅛(625π) square units.
