If seven evenly matched competitors run a race, in how many ways can they place 1st, 2nd, and 3rd?

*Solution to yesterday’s problem:*

Let’s use an annotated version of the diagram:

Knowing that the side length of the total square is 2 ft, we can say that the segments to either side of the octagon’s sides are 0.5 ft each. This makes four triangles, each with a base and height of 0.5 feet. Expressing their combined area gives

.

Simplifying,

The final answer is that there is *0.5 square feet* left in the square.

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