Mathematics Question and Solution
Let P be the required area.
Calculating P.
a² = 6²+3²
a² = 45
a = √(45)
a = 3√(5) cm.
b = a-x
b = (3√(5)-x) cm.
tanc = 6/3
c = atan(2)°
d = atan(½)
f = 90+d
f = (90+atan(½))°
Calculating x
½*3(3√(5)-x)sin(90+atan(½)) = ½*(3+3)xsin(atan(2))
9-1.3416407865x = 2.683281573x
4.0249223595x = 9
x = (9/4.0249223595)
x = 2.2360679775 cm.
Calculating area S.
It implies;
Area S = 0.5*2.2360679775*6sin(atan(2))
Area S = 6 cm²
The required area, P is;
½(3+6)*6-2S
P = (9*3)-2(6)
P = 27-12
P = 15 cm²
