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

Study concepts, example questions & explanations for Intermediate Geometry

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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 .


Possible Answers:

Correct answer:



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)?

Possible Answers:

Correct answer:


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 :

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