Math CentralQuandaries & Queries


Question from sarah, a student:

i'm trying to find the area of a regular pentagon with 200m sides, I've split it into 5 triangles so i don't know either sizes of the lengths and i need to find the height!

Hi Sarah,

Each of your 5 isosceles triangles has central angle of 360/5 = 72 degrees. Hence by bisecting this angle you get the diagram below.


Thus tan(36o) = h/100 and hence you can find h.

Stephen has done this in much more generality and developed an expression for the area of any regular polygon. To see what he did go to the Quandaries and Queries page on Math Central and use the Quick Search to search for the term polygon area.


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