Mathematics Question and Solution
Calculating the area of the regular pentagon not enclosed by the blue circle.
πr² = 288π
r² = 288
r = √(288)
r = 12√(2) cm.
r is the radius of the ascribed black circle.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b = 180-2(½(a))
b = 180-108
b = 72°
c = ½(108)
c = 54°
sinc = d/r
d = 12√(2)sin54
d = 13.7294736676 cm.
d is the radius of the blue inscribed circle.
It implies;
Area regular pentagon not enclosed by the blue circle is;
5(area triangle with height 12√(2) cm and base 12√(2)sin72 cm) - Area circle with radius 13.7294736676 cm.
= 5(½*12√(2)*12√(2)sin72)-(π*13.7294736676²)
= (5*144sin72)-(592.185336903)
= 684.760691733-592.185336903
= 92.57535483 cm²
