# geometry

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I am having a hard time determining what formula I need to solve the following: On a hexagonal window the height is 1.3m. Find the width.Do I use the pythagreom theorem (but I have only one known number) or do I use the formula 6(1/2as)? I'm confused. The book says the answer is 2.6/square root of 3 or 1.5m. How was this obtained?

• geometry -

Draw a regular hexagon. It consists of six equilateral triangles. Each has a "height" of 0.65m (measured between two opposite sides). The "width" of the hexagon, measured between opposite corners, is 2R, where R is the radius of the circumscribed circle, which is 0.65/sin60 = 0.75056 m
Double that for the width: 1.5011 m
Round off to 1.5.

• geometry -

thank you. I knew the equilateral triangles played a part, but I was confused because only one measurement was given.

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