Mathematics Question and Solution
Let the height of the yellow area trapezoid be a.
Calculating a.
tan72 = a/b
b = (a/tan72) cm.
c = 2b
c = (2a/tan72) cm.
d = 8+c
d = (8+(2a/tan72)) cm.
It implies;
½*a(8+(8+(2a/tan72))) = 56.23
a(16+0.64983939247a) = 112.46
0.64983939247a²+16a- 112.46 = 0
Therefore;
a = 5.70627 cm.
d = (8+(2a/tan72))
d = 11.70815903005 cm.
tan18 = e/5.70627
e = 1.85407951502 cm.
f = 2e
f = 3.70815903005 cm.
(g/sin36) = (8/sin108)
g = 4.94427191 cm.
sin72 = h/8
h = 7.60845213036 cm.
i = h-a
i = 1.90218213036 cm.
Therefore;
Area Green in cm² to 2 decimal places is;
0.5*1.90218213036(4.94427191+3.70815903005)
= 8.22924975917 cm²
≈ 8.23 cm²
