Write an explanation that justifies this statement: The area of a regular polygon is half the produc of the apothem and the perimeter

Question

anonymous · Answer

wats area of polygon formula?

anonymous · Answer

1/2ap. I know that's the formula, but I need to justify why that is.

anonymous · Answer

You can inscribe n congruent triangles into a regular n sided polygon, the apothem will be the height of each triangle and if we sum up the areas and factor out the apothem and a factor of 1/2 we will be left with the perimeter.

anonymous · Answer

Thus the area of an n sided regular polygon is equal to half the apothem multiplied by the polygons perimiter.

anonymous · Answer

Thanks! :)