Mathematics Question and Solution
a = ⅕(180(5-2))
a = 108°
b = 180-108
b = 72°
sin72 = c/6
c = 5.7063390978 cm.
cos72 = d/6
d = 1.8541019662 cm.
e = 1.8541019662+6
e = 7.8541019662 cm
f² = 7.8541019662²+6²-2*7.8541019662*6cos108
f = 11.2610625384 cm.
(11.2610625384/sin108) = (6/sing)
g = 30.4463843172°
h = 90-30.4463843172
h = 59.5536156828°
i = 180-18-59.5536156828
i = 102.4463843172°
(5.7063390978/sin102.4463843172) = (j/sin59.5536156828)
j = 5.0378552605 cm.
k² = 6²+6²-2*6*6cos108
k = 9.7082039325 cm.
l = 90-18
l = 72°
Therefore, area shaded (orange area) is;
Area triangle with height 6 cm and base 6sin108 cm + Area triangle with height 9.7082039325 cm and base 5.0378552605sin72 cm.
= 0.5*6*6sin108+0.5*9.7082039325*5.0378552605sin72
= 17.1190172933+23.2573862969
= 40.3764035902 cm²
