# Intermediate Geometry : How to find the length of the diagonal of a pentagon

## Example Questions

### Example Question #1 : How To Find The Length Of The Diagonal Of A Pentagon

In the pentagon below, the length of is one-third that of . Find the length of diagonal .      Explanation: Start by using the Pythagorean theorem to find the length of .  Since is one-third the length of , we know that the length of must be .

Now, notice that the pentagon is made up of one rectangle and two right triangles.

Focus on rectangle . We can find the length of by adding together the lengths of and . Since we are working with a rectangle, we know that . Thus, we can use the Pythagorean Theorem again to find the length of .  Make sure to round to two places after the decimal.

### Example Question #11 : Pentagons

What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?      Explanation:

Let be the length fo a diagonal.

One interior angle of a pentagon measures A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and ; the side of length is opposite the angle of measure , and each side of length 20 is opposite an angle of measure .

The Law of Sines helps us to determine :  ### All Intermediate Geometry Resources 