Mathematics Question and Solution
Calculating green area.
c² = a²+b²
c = √(4²+6²)
c = √(52)
c = 2√(13) units.
c = 7.2111025509 units.
d = 90-atan(4/6)
d = atan(3/2)°
e = 180-2d
e = (180-2ata(3/2))°
sin(0.5(180-2ata(3/2))) = (0.5*2√(13))/f
f = 6.5 units.
f is the radius of the half circle.
g = 180-2(180-2atan(3/2))
g = 180-360+4atan(3/2)
g = (4atan(3/2)-180)
g = 45.2397298961°
Therefore, green area is;
Area sector with radius 6.5 units and angle 45.2397298961° - Area triangle with height 6.5sin45.2397298961 units and base 6.5 units.
= (45.2397298961π*6.5*6.5/360)-(0.5*6.5*6.5sin45.2397298961)
= 16.6799248073-15
= 1.6799248073 square units.
