Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the regular heptagon be 1 unit.
Therefore;
Area Regular Heptagon is;
7/(4tan(180/7))
= 3.633912444 square units unit.
Area Blue is;
Area triangle with two equal lengths 2.24697960372 units, each and angle (180/7)° - Area triangle with lengths 1 unit and 1.08208834613 units, and angle (270/7)° - Area triangle with lengths 0.80193773581 units and 1 unit, and angle (180/7)°
= ½(2.24697960372)²sin(180/7) -½(1.08208834613*1)sin(270/7) - ½(0.80193773581*1)sin(180/7)
= 1.09532156689 - 0.33733552426 - 0.17397387168
= 0.58401217095 square units.
Therefore;
Area Blue ÷ Area Regular Heptagon to 2 d.p. is;
0.58401217095 ÷ 3.633912444
= 0.1607116792
≈ 0.16
