How would a circumscribed hexagon compare to the area of a circle? underestimate of the circle
overestimate of the circle
same area as the circle
does not compare

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Explanation:

A circumscribed polygon always surrounds the circle, so the circumscribed hexagon will have an area larger than the circle. This is why we have an overestimate. In contrast, an inscribed hexagon would underestimate the area. The idea is that as the number of sides n increases, the under and over estimates will slowly converge to a single number which is the area of the circle.

It's basically a guessing game where you either go too high or too low, and eventually hit the target after enough tries.

Check out the diagram below to see what a circumscribed hexagon looks like. Note how the hexagon is as small as possible without any line segments going inside the circle; put another way, the circle doesn't spill outside the hexagon.

astronomers is your final answer! : )