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As shown above, the yellow polygon is surrounded by seven unit regular heptagons. If the area of the yellow polygon can be expressed as
where are integers, input as your answer.
The answer is 8.
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1 solution
The yellow polygon can be divided into 3 magenta unit rhombi of interior angle 7 π and 5 orange unit rhombi of interior angle 7 3 π :
Since each magenta rhombus has an area 2 ⋅ 2 1 ⋅ 1 ⋅ 1 ⋅ sin 7 π = sin 7 π and each orange rhombus has an area 2 ⋅ 2 1 ⋅ 1 ⋅ 1 ⋅ sin 7 3 π = 7 3 π , the total area is
3 sin 7 π + 5 sin 7 3 π
where A = 3 , B = 0 , C = 5 gives A + B + C = 8 .