What is the name for a five sided shape and how do you calculate the area of the same?

Answer 1

The shape you speak of - the polygon that has five sides - is the pentagon. This, or any other polygon, may be described as 'regular' when it has equal sides and vertex angles. As you might guess, all others would be called 'irregular'. Not every interior angle has to be less than 180 degrees.

To calculate the whole area of the interior of a pentagon (or any polygon) we can first subdivide it into triangles by drawing dotted lines between non-adjacent vertices.

Heron's Formula (see: en.wikipedia.org/wiki/Heron%27s_formula) can be applied to find the area of any triangle thus created, as long as the lengths of its three sides are known. Then, of course, the sum of all those separate triangular areas will be equal to the area of the whole pentagon.

We are not able to make diagrams on this site, so this explanation is wordy and very limited in scope. However, there is a demonstration of this calculation for a pentagon (with diagrams) here: mathcentral.uregina.ca/QQ/database/QQ.09.06/graham1.html

The area of a regular polygon is given by the formula below.

Area = (½)(apothem)(perimeter)

Here is the definition of 'apothem':

The line segment from the center of a regular polygon to the midpoint of a side, or the length of this segment. This is the same as the inradius; that is, the radius of a regular polygon's inscribed circle.

Answer 2

Irregular polygon