Intermediate Geometry : Pentagons

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #28 : How To Find The Area Of A Pentagon

In the figure below, find the area of the pentagon if the length of  is one-fourth the length of .

2

Possible Answers:

Correct answer:

Explanation:

2

Start by figuring out the lengths of  and .

Let  be the length of . From the question, we then write the length of  as .

From the figure, you should see that .

Plug in the variables and solve for .

So then the length of  must be , and the length of  must be .

Now, to find the area of the pentagon, notice that we can break the shape down to one rectangle and two right triangles.

Next, find the area of rectangle .

Next, find the area of the right triangles.

For triangle ,

For triangle ,

Add up the component areas to find the area of the pentagon.

Learning Tools by Varsity Tutors