SOLUTION: If a hexagon has sides measuring 1 metre 65 cm what is the width across the widest part of the hexagon? This is a practical problem because we would like a garden summerhouse but

Question 961670: If a hexagon has sides measuring 1 metre 65 cm what is the width across the widest part of the hexagon? This is a practical problem because we would like a garden summerhouse but it has to fit into a specific space, a curved stone wall and therefore "set in stone". I have drawn a diagram for myself which I think shows the width across the widest part of the figure is more than 1 m 65 cm but I do not know how to work out what will be the best use of the space.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1 meter 65 centimeters is equal to 165 centimeters because 1 meter is equal to 100 centimeters.

so the width of one side of your pentagon is 165 centimeters.

i believe this will help you.

you can probably do the math, but this is so much easier.

http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php

if you plug in 165 centimeters as the length of the side (called "a"), then you will get:

the height of the pentagon would be 113.552 + 140.357 = 253.909 centimeters.

they do not show you the width and you can't really see what the width is from the diagram.

that diagram, by the way, is shown below:

$$$

to find the width, you will probably need a little trigonometry.

see the following picture.

$$$

the height is r + R which is equal to 253.909

the width is AB in the second picture which is equal to 266.975

the width is the largest measurement.

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