Mathematics Question and Solution
b = (180(12-2))/12
b = 1800/12
b = 150°
b is the single interior angle of the regular dodecagon.
2c+2(150) = 360
2c = 60
c = 30°
d = 150-15-30
d = 105°
2e+3(150) = 180(5-2)
2e = 540-450
2e = 90
e = 45°
f = e-15
f = 30°
g = 180-d-f
g = 180-105-30
g = 45°
It implies;
(h/sin105) (2√(2)/sin30)
h = 5.4641016151 units.
j = 150-15-45
j = 90°
k = 180-105-30
k = 45°
(l/sin45) = (2√(2)/sin105)
l = 2.0705523608 units.
l is the side length of the regular dodecagon.
m² = 2(2.0705523608)²-2(2.0705523608)²cos150
m = 4 units.
Therefore, area shaded (area pink) is;
Area triangle with height 4 units and base 5.4641016151 units + Area triangle with height 2.0705523608 units and base 2.0705523608sin150 units.
= (½*4*5.4641016151)+(½*2.0705523608*2.0705523608sin150)
= 12 square units.
