Mathematics Question and Solution
Let the side length of the regular pentagon be a.
b = ⅕(180(5-2))
b = 108°
b is the single interior angle of the regular pentagon.
c = 108-90
c = 18°
d = (180-2(18))
d = (180-36)
d = 144°
e = ½(f)
e = ½(144)
e = 72°
notice!
Radius of the circle is 1 unit.
It implies;
sin72 = 0.5a/1
0.5a = sin72
a = 2sin72 units.
a is the side length of the regular pentagon which is also the side length of the inscribed square.
It implies;
Area square exactly is;
a²
= (2sin72)²
= 4sin²(72) square units.
= 3.6180339887 square units exactly in decimal.
Or
cos18 = 0.5a/1
0.5a = cos18
a = 2cos18 units.
a is the side length of the regular pentagon which is also the side length of the inscribed square.
It implies;
Area square exactly is;
a²
= (2cos18)²
= 4cos²(18) square units.
= 3.6180339887 square units exactly in decimal.
