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The circus tent

A regular octagon is coloured as shown. What fraction of its area is red?

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Solution

Exactly 1/2 of the figure is red.

First, notice that all sides have equal length. For convenience we scale it to 1. Now the distance from a side to the regular octagon centre is h and the total area is 8*h/2=4h.

The area of the middle red triangle is easily seen to be 2h/2=h. The others have area h1/2 and h2/2 respectively. Now since h1+h2=2h, they add up to also h.

Therefore the red area is 2h, which is half the total.

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