Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular octagon be 1 unit.
(a) Calculating alpha exactly. Let it be x.
x = atan(1/(√(2)+1)
x = 22.5°
(b) Calculating Area Yellow ÷ Area Green exactly.
Area yellow is;
Area triangle with height √(2) units and base (2-√(2)) unit.
= ½*√(2)*(2-√(2))
= (√(2)-1) square units.
Area green is;
Area trapezoid with parallel sides 1 unit and √(2) units, and height ½√(2) unit.
= ½*½√(2)(√(2)+1)
= ¼(2+√(2)) square units.
It implies;
Area Yellow ÷ Area Green exactly is;
(√(2)-1) ÷ ¼(2+√(2))
= 2(3√(2)-4)
