Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
11th March, 2025

Sir Mike Ambrose is the author of the question 

Let the side of the regular Pentagon be 2 units.


Therefore;


Area orange is;


Area triangle with height 1.7013016167 units and base 1.8345763534sin(18) units


= ½*1.7013016167*1.8345763534sin(18)

= 0.48224693327 square units.


Area blue is;


Area trapezoid with parallel sides 0.21654236465 units and 1 unit, and height 1.9021130326 units.


½*1.9021130326(0.21654236465+1)

= 1.15700054326 square units.


It implies;


Area Orange ÷ Area Blue to 2 decimal places is;


0.48224693327 ÷ 1.15700054326

= 0.41680787108

≈ 0.42

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