Why Do We Measure Perimeter?
Have you ever walked around a playground? Or put a fence around a garden? People have been measuring the distance around shapes for thousands of years!
The word perimeter comes from two Greek words: peri (meaning "around") and metron (meaning "measure"). So perimeter literally means "measure around." Pretty cool, right?
On the ISEE test, you will see diagrams of shapes with side lengths labeled. Your job is to find the perimeter. Let's learn how!
Core Ideas About Perimeter
Before we start calculating, let's learn the big ideas. These four rules will help you solve every perimeter problem!
Perimeter = Total Distance Around
Add Up All the Sides
Count Every Side
Units Stay the Same
See It: Perimeter in a Picture
Let's look at a rectangle with labeled sides. Follow the arrows around the shape. That path is the perimeter!
Notice how the arrows go all the way around the rectangle. We add each side as we go: top (12 ft), right side (8 ft), bottom (12 ft), and left side (8 ft). The total is 40 feet.
The Perimeter Formulas
For any shape, you can always just add all the sides. But for common shapes, there are shortcuts. These formulas save you time!
Different Shapes, Same Idea
The ISEE may show you rectangles, squares, triangles, or even L-shaped figures. Let's look at several shapes and their perimeters side by side.
Notice the L-shaped figure at the bottom left. It has 6 sides, not 4! On the ISEE, you might see shapes like this. The trick is to count every side carefully.
Step-by-Step Example
Let's work through a problem together, step by step. Imagine you see this on the ISEE:
A rectangle has a length of 14 cm and a width of 9 cm. What is the perimeter?
Common Mistakes to Avoid
Even smart students make mistakes on perimeter problems. Here are the most common ones and how to avoid them.
| Mistake | Why It Happens | How to Fix It |
|---|---|---|
| Forgetting a side | You add only 3 sides of a rectangle instead of 4. | Count the sides first. Put a check mark on each side as you add it. |
| Mixing up perimeter and area | You multiply length × width instead of adding all sides. | Remember: perimeter = add. Area = multiply. Perimeter is the fence; area is the grass inside. |
| Missing unlabeled sides | The diagram doesn't label every side, so you skip one. | Use what you know. Opposite sides of a rectangle are equal. Figure out missing sides. |
| Wrong addition | Simple adding mistakes when no calculator is allowed. | Double-check your addition. Add the numbers a second time to make sure. |
Perimeter of Trickier Figures
Sometimes the ISEE gives you shapes that aren't plain rectangles. You might see L-shapes or figures with missing side labels. Don't worry — you can handle them!
| Simple Shapes | Trickier Shapes |
|---|---|
| All sides are labeled | Some sides may be missing labels |
| 3 or 4 sides | 5, 6, or more sides |
| Just add the numbers you see | Figure out missing sides first, then add |
| Example: rectangle, triangle | Example: L-shape, T-shape, U-shape |
To find a missing side on an L-shape, look at the sides that run in the same direction. If the full top is 10 and one part of the top is 6, the other part must be 10 − 6 = 4.
Practice Problems
Time to practice! Remember: no calculator, just like on the real ISEE. Read each problem carefully, and add up all the sides. You've got this!