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Shaded Hexagon

Problem

Two congruent equilateral triangles, each with an area equal to 36 cm2, are placed on top of each other so that they form a regular hexagonal overlap.


Find the area of the hexagon.


Solution

The triangles can be split up as follows:


It can be seen that the shaded area is 6/9 of one triangle, that is 2/3 of 36 = 24 cm2.

Must the triangles be equilateral?
What will the area of the overlap be if two squares, each with an area of 36 cm2, are overlapped in the same way to form an octagon?
Is the octagon regular?

Problem ID: 149 (Feb 2004)     Difficulty: 1 Star

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