Mathematics Question and Solution
Let the regular octagon side be 2 units.
Area Octagon is;
½(8*2)*(2/(2tan(180/8)))
= 8/(tan(180/8))
= 19.31370849898 square units.
Calculating Area Red.
a = ⅛(180*6)
a = 135°
Let the square side be b.
Calculating b.
(b/tan60)+(b/tan45)+b = 2
b = 2/(1+(1/tan60)+(1/tan45))
b = 0.77599076226 unit.
Area Red is;
b²
= 0.77599076226²
= 0.60216166311 square units.
Therefore;
Area Octagon ÷ Area Red to 2 decimal places is;
19.31370849898 ÷ 0.60216166311
= 32.07395900816
≈ 32.07
