*Contributor: Briana Pincherri. Lesson ID: 11315*

Oh no! A side is missing! Does that mean your quadrilateral's going to collapse? No, but we need to find the length of a side when we have the perimeter or area. Learn how with videos and online help!

categories

subject

Math

learning style

Visual

personality style

Lion, Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Your team needs a new practice field ASAP! Could you figure out the dimensions of the field? Do you know what math would be involved to figure out something like this?

If you are viewing this lesson, you have already mastered the concepts of area and perimeter in the first **Related Lessons** of this series and are ready to try more challenging concepts.

If that sounds like you, then you are in the right place! But first, let's start with a quick review on area and perimeter. (If you need more of a review first, check out the **Related Lessons** in the right-hand sidebar.) Begin by drawing a rectangle or square on a piece of paper, then explain the difference between area and perimeter to your teacher or parent. Ready? Go!

When you discussed the quadrilateral, hopefully you told them:

- Perimeter is the distance around the OUTSIDE your shape (for example, the length of fence needed to fully enclose a yard).
- Area is the measurement INSIDE your shape (for example, the total amount of land inside the fenced area).

Remember, with perimeter you can simply ADD the sides together to get it. The only formal formula for the perimeter of a polygon is for a rectangle: A = 2L + 2W. Beyond that, you can just *add, add, add the sides to get the perimeter*! (Try singing that part out loud to "Row, Row, Row Your Boat")

The area formulas are as follows:

Square = L x W (Length x Width)

Rectangle = L x W (Length x Width)

Triangle = ½ b x h (½ x base [bottom] x height [line perpendicular from base to top])

You can use these formulas to find the total area of shapes, but you can also use them when you know the area and need to find a missing side length!

Watch this short video, *Finding Missing Side Lengths of a Rectangle, Given Perimeter*, by Matt Honigman:

Hopefully, you noticed that, for area, you are still using the same formula. You can substitute in everything that you know and solve for what is missing. Most times, this just means your are going to end with a last step of DIVIDING instead of multiplying.

Example: The area of a rectangle is 88 ft. The width of it is 8 ft. What is the length of it?

A = L • W

88/8 = L • 8/8 → Divide the total area by the side you know:

L = 11 ft. → The length is 11 ft.

With perimeter, it can be even easier! You will want to take a total perimeter and subtract any side lengths that you know. By doing this, you can get to the missing side length.

Example: You have a pentagon (5 sides) with a total perimeter of 21 in. The sides you know are 3 in, 6 in, 2 in, and 4 in. What is the length of the missing side?

Total perimeter – Sides = Missing Side

21 in. – 3 in. – 6 in. – 2 in. – 4 in. = 6 in.

The missing side length in the pentagon is 6 in.

Let's continue with some practice.

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