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 Regular pentagon QRSTU has a side length of 12 centimeters and an area of 248 square centimeters. Regular pentagon VWXYZ has a perimeter of 140 centimeters. I need to find its area.

Hi there.

When you have similar shapes and the ratio of the linear dimensions is x, then the ratio of the area dimensions is x2.

What I mean is this: The side length of the second pentagon is 28. So the ratio of the linear dimensions is 28/12 = 7/3.
So the ratio of the areas is (7/3)2. This means the area of the second pentagon is the area of the first times this ratio:

A = (248) (7/3)2.

You can also calculate it the longhand way. See the following examples:
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/dana1/dana1.html
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/sarah1.html
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/susan1.html

Or just type pentagon into the Quick Search.

Cheers,
Stephen La Rocque

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