Mathematics Question and Solution
Calculating inscribed shaded area green.
a = ⅛*180(8-2)
a = ¼*180*3
a = 135°
a is the single interior angle of the regular octagon.
2b² = 4²
b² = 8
b = 2√(2) units.
c = 2b
c = 4√(2)units.
Therefore, green inscribed area is;
Area triangle with height 4√(2) units and base 4√(2)sin45 units - Area triangle with height and base 2√(2) units respectively.
= (½*4√(2)*4√(2)sin45)-(½*2√(2)*2√(2))
= 8√(2)-4
= 4(2√(2)-1) square units.
= 7.313708499 square units.
