Area of a pentagon?

Question

how do you calculate the area of a pentagon?

Answer 1

Break the pentagon down into smaller shapes whose areas you know how to calculate. By being creative and drawng a few horizontal or vertical lines from the vertices, you can break it down into squares and triangles whose areas are easy to calculate and then simply add together

An alternative method can be found here but it applies only to regular (uniform) pentagons:
http://www.dummies.com/WileyCDA/DummiesArticle/id-1195.html

Rob

Answer 2

Assuming you're talking about a regular pentagon, all you have to do is find the area of the five regular triangles which make it up.

First draw straight lines from each vertex to the center to get the five triangles. Now you have to figure out what the angles are: since they all meet at the center, this angle is 360/5, or 72 degrees, and therefore the outer angles of each triangle are (180-72)/2, or 54 degrees.

The area of a triangle is 1/2 * base * height (obvious since a triangle is essentially half of a rectangle). The height or altitude of a triangle is the perpendicular distance from its base to the opposite vertex, so we draw a line from the midpoint of the base (one edge of the pentagon) to the center and find its length.

Now we have a right triangle to work with and the rest is easy, but I won't do it for you. The length of the perimeter is known and from that you can find the (equal) lengths of the other sides of the triangles. The height can be found using either sines or cosines, then just do the arithmetic for the answer.

Answer 3

the area of the regular polygons (including the pentagon) is
1/2*apathem*P(perimeter of the polygon)