Find the area of a regular pentagon whose apothem is 25.1 and perimeter is 182 mm

Divide the pentagon into 5 equal triangles each with an outermost side length of 182/5 or 36.4 

you also know that the height of all these triangles will be the length of the apothem or 25.1 

so you can find the area of one triangle using A= 1/2 bh 

this gives you 456.82, then multiply this by 5 as to include all 5 triangles in the pentagon 

this gives you 2284.1mm^2 and that is your answer

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