How do you calculate the area of a regular pentagon

When the only information you have is that all its sides are 10cm? I'm lost :(

Divide it into 5 triangles using each vertex and the "center", then find the area of one of them and multiply by 5.
It is regular so all of these areas are congruent.

Step 1: Find the measure of an exterior angle of the pentagon

Step 2: Partition the Pentagon into 5 triangles by connecting each vertex to the "center" of the pentagon.

Step 3: Find the angle measure of the base angles for each of those triangles.
You only have to do one since they are all symmetric ("regular" pentagon)

Then you should have a triangle with 2 angles known along with a side length between them.

Step 4, find the lengths of the segments from the vertices to the "center"
Once again, since it is a regular pentagon, you only need to do one.
(I think the easiest way to do this is using the Law of Sines)

Step 5, draw a line through the "center" perpendicular to the side of the pentagon.
This divides the triangle into 2 congruent right triangles.
(we are trying to find the altitude of the triangle)

Step 6: Find the altitude.
Sin [ base angle ] = altitude / "radius"

Step 7: Calculate the area of 1 triangle.
Remember A of triangle = 1/2 * base * altitude.

Step 8: Calculate area of pentagon.
Area of pentagon = 5 * area of each triangle.

Whew!

I hope this helps.

A pentagon having 5 sides is made up of 5 triangles with central angles of
180/5 = 72 degrees. The length of the sides is l = 2 R sin(72/2)
The distance from center to midpoint of the side is h = R cos(72/2).
The area of the triangle formed by R, h, l is 1/2 * h * l . There 10
of these triangles in the pentagon . So for R = 1 the area is
A = 10 * h * l or A = 10 * 1/2 * cos(36) * 2 * sin(36)...
A = 10 * 1/2 * 0.80902 * 2 * 0.58779 = 4.75528

ur go 2 say l x b =area