Mathematics Question and Solution
Let BC be 1 unit.
AB = 2 units.
tan18 = a/2
a = 0.6498393925 units.
a is the radius of the inscribed circle.
Area inscribed circle is;
π(0.6498393925)²
= 1.3266670448 square units.
b = ½(2+1)
b = 1.5 units.
b is the radius of the ascribed semi circle.
c = 180-72
c = 108°
(1.5/sin36) = (d/sin108)
d = 2.4270509831 units.
e = 2.4270509831-2
e = 0.4270509831 units.
Calculating Area Red.
It is;
0.5*0.6498393925*0.4270509831
= 0.1387572757 square units.
It implies;
Area Red ÷ Area Circle to 3 decimal places is;
0.1387572757÷1.3266670448
= 0.1045908815
≈ 0.10
