Mathematics Question and Solution
Calculating Green Area.
a = 2*4
a = 8 units.
a is the radius of the ascribed quarter circle.
b²+4² = 8²
b² = 64-16
b = √(48)
b = 4√(3) units.
tanc = 4√(3)/4
c = atan(√(3))°
c = 60°
Therefore, green area is;
Area sector with radius 8 units and angle 60° - Area triangle with height 4√(3) units and base 4 units - Area quarter circle with radius 4 units.
= (60π*8*8/360)-(½*4√(3)*4)-(¼*4*4π)
= ⅓(32π)-8√(3)-4π
= ⅓(32π-12π-24√(3))
= ⅓(20π-24√(3)) square units.
= 7.0875445634 square units.
