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Printjmc
geometry intermediate
Problem
In regular octagon , and are midpoints of and respectively. Compute . ( denotes the area of polygon .) 
Solution
We connect the midpoints of all opposite sides and we connect all opposite vertices:
Because of symmetry, these lines split the octagon into 16 congruent regions. Quadrilateral is made up of three of these regions and pentagon is made up of five of these regions. Hence, .
Because of symmetry, these lines split the octagon into 16 congruent regions. Quadrilateral is made up of three of these regions and pentagon is made up of five of these regions. Hence, .
Final answer
\frac{3}{5}