1 · Perimeter: the walk around the edge
Imagine an ant walking all the way around a shape and coming back to where it started. The distance it walks is the perimeter.
To find it, add up every side. This rectangle is 5 long and 3 tall: 5 + 3 + 5 + 3 = 16. The ant walks 16 units.
2 · Every side counts, even the ones with no number
A rectangle has 4 sides, and opposite sides are the same length. If you only see two numbers, the other two sides match them.
This rectangle shows 6 and 2. The hidden sides are also 6 and 2. Perimeter: 6 + 2 + 6 + 2 = 16.
3 · Squares, triangles, and any shape at all
A square has 4 sides that are all the same. Side 4 means 4 + 4 + 4 + 4 = 16, or 4 × 4 = 16.
Perimeter works for any shape. A triangle with sides 3, 4, and 5 has perimeter 3 + 4 + 5 = 12. Just add every side once.
4 · Area: how many squares fit inside
Area is how much space is inside a shape. We measure it by counting the unit squares that cover it.
Count the squares in this rectangle: 12. Its area is 12 square units.
5 · Count by rows
Counting one square at a time is slow. Count a row instead, then count how many rows.
Each row has 4 squares, and there are 3 rows: 4 + 4 + 4 = 12. That is the same as 3 × 4 = 12.
6 · Area = length × width
For any rectangle, area = length × width. No grid needed, just the two numbers.
This rectangle is 6 long and 2 wide: 6 × 2 = 12 square units. The faint lines show the 12 squares hiding inside.
7 · Same area, different perimeter
These three rectangles all have area 12: 1 × 12, 2 × 6, and 3 × 4.
But their perimeters are different: 26, 16, and 14. The long skinny one has the longest walk around. Area and perimeter are two different things!
8 · Same perimeter, different area
Now the other way around. These rectangles all have perimeter 12.
1 × 5 holds 5 squares, 2 × 4 holds 8, and 3 × 3 holds 9. Same fence, different amount of garden inside.
9 · Odd shapes: cut them into rectangles
This L shape is not a rectangle, but you can cut it into two rectangles along the dotted line.
The bottom part is 5 × 2 = 10. The top part is 2 × 3 = 6. Add them: 10 + 6 = 16 square units. (Or just count the squares!)
10 · Perimeter of odd shapes
For perimeter, the ant still walks every edge. Go around the L and add: 5 + 2 + 3 + 3 + 2 + 5 = 20.
Fun fact: a 5 × 5 square also has perimeter 20, but its area is 25, and the L only has 16. The notch cut out some area without changing the walk around.
11 · Units and square units
Perimeter is a length, so it uses plain units: inches, feet, centimeters. "The fence is 20 feet."
Area counts squares, so it uses square units: square inches, square feet, square centimeters. "The rug covers 20 square feet."
12 · Working backwards
Sometimes you know the answer and need a missing side.
A rectangle has area 20 and one side is 4. What is the other side? Think: 4 × ? = 20, so ? = 5.
A square has perimeter 20. All 4 sides are equal, so each side is 20 ÷ 4 = 5. You are ready for the test! 🎉
Ready to check what stuck?
Take the free 24-question test. It starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.