Finding the area of a regular polygon when you know the side length
Find the area of an sided regular polygon if you know the side length,
.

Find the of the triangle in terms of
and theta.

Remember the area of a triangle is
Hence,
And
Therefore
There are triangles in an
sided polygon
(1)
Find the area of a hexagon with side length 10cm.![]() ![]() ![]() |
Finding the area of a polygon if you know the inradius or the apothem

The apothem and the inradius are the same. It is the radius of the incircle.
Find the area of the triangle in terms of and theta.
And
Hence for an sided polygon
(2)
Find the area of a regular pentagon with apothem 4.5cm![]() ![]() |
Finding the area of a regular polygon given the circumradius

The circumradius is the radius of the circumscribed circle ( in the diagram above)
Remember the area of triangle formula
Hence,
Hence, for an sided polygon
(3)
Find the area of a regular octagon inscribed in a circle of radius 10cm.![]() ![]() |