Mathematics Question and Solution
Let Phi be a.
let Beta be b.
Notice.
b = 2a
And b = 45°
It implies;
2a = 45
a = 22.5°
Let CF = c.
tan22.5 = c/d
d = c/tan22.5 units.
d is CE.
Therefore;
c+d = 12
c+(c/tan22.5) = 12
3.4142135624c = 12
c = 3.5147186258 units.
d = c/tan22.5 units.
And c = 3.5147186258 units.
d = 3.5147186258/tan22.5
d = 8.4852813743 units.
Calculating BC = CD = DE, the side length of the square.
Let it be e.
2e² = 8.4852813743²
e² = 36 square units.
Where e² is the area of the square.
