Mathematics Question and Solution
Calculating Area Blue.
a = ⅙*180(6-2)
a = 120°
a is the interior angle of the ascribed regular hexagon.
b² = 5²+5²-2*5*5cos120
b² = 50+25
b = √(75)
b = 5√(3) units.
b is the height of the regular hexagon.
Therefore, are blue is;
Area regular hexagon - 2(area sector with radius 2.5 units and angle 120°)-4(area triangle with height 2.5 units and base 2.5sin60 units)-2(area sector with radius 2.5 units and angle 60°).
((5√(3)*5)+(2.5*5√(3)))-2(120π*2.5²/360)-4(0.5*2.5*2.5sin60)-2(60π*2.5²/360)
= (25√(3)+12.5√(3))-⅓(12.5π)-6.25√(3)-⅓(6.25π)
= 37.5√(3)-6.25√(3)-⅓(12.5π)-⅓(6.25π)
= 31.25√(3)-⅓(18.75π)
= ⅓(93.75√(3)-18.75π) square units.
= 34.4916336516 square units.
