Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Green ÷ Area Yellow to 3 d. p.
Let the side length of the regular pentagon be 2 units.
Therefore the angle theta is;
asin(2sin42÷1.65418183057)
= 54°
Area green is;
Area triangle with height (1/cos54) units and base 2.45859333557sin12 units - Area triangle with height 2cos54 units and base 2cos54*tan12 units
= (0.5*2.45859333557sin12*(1/cos54)) - (0.5*2cos54*2cos54*tan12)
= 0.43482742672 - 0.14687297185
= 0.28795445487 square units.
Area yellow is;
Area triangle with height 2.45859333557 units and base 2sin42 units.
= 0.5*2.45859333557*2sin42
= 1.64512004942 square units.
Therefore;
Area Green ÷ Area Yellow to 3 d. p. is;
0.28795445487 ÷ 1.64512004942
= 0.17503552703
≈ 0.175
