Math CentralQuandaries & Queries


Question from Jenna, a student:

I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given.
Thank you

Hi Jenna,

If you construct lines from each vertex to the centre you divide the pentagon into 5 congruent triangles.


The area of the pentagon is 5 times the area of each triangle and the area of each triangle is

1/2 × base × height = 1/2 × (side length) ×apothem.


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