Mathematics Question and Solution.
Calculating the area of the inscribed square.
a = ½(45)
a = 22.5°
b = ½(180-45)
b = ½(135)
b = 67.5°
cos22.5 = 6/c
c = 6.4943532018 units.
Let d be the side length of the inscribed square.
e² =2d²
e = √(2)d unit.
e = 1.4142135624d units.
(√(2)d/sin45) = (f/sin67.5)
f = 1.847759065d units.
(g/sin45) = (d/sin67.5)
g = 0.7653668647d units.
d is;
c = f+g
1.847759065d+0.7653668647d = 6.4943532018
2.6131259297d = 6.4943532018
d = 2.4852813743 units.
Again, d is the side length of the inscribed square.
Therefore, area inscribed square is;
d²
= 2.4852813743²
= 6.1766235093 square units.
= 6.18 square units to 2 decimal places.
