Area & Perimeter
Area measures the space inside a shape; perimeter measures the distance around the outside of a shape.
Reading is good — doing is better. Practice Area & perimeter as an interactive lesson.
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Area is how many square units fit inside a flat shape, like how many square tiles cover a floor. Perimeter is the total length of all the sides added together, like how much fence you would need to go all the way around a yard.
Remember the rule
Area of a rectangle = Length × Width. Perimeter of a rectangle = (Length + Width) × 2, or just add all four sides together.
Key words
- Area
- The amount of space inside a flat shape, measured in square units like square inches or square centimeters.
- Perimeter
- The distance all the way around the outside of a shape, found by adding up all the side lengths.
- Square unit
- A tiny square used to measure area — for example, one square inch is a square that is 1 inch on every side.
- Side
- One of the straight lines that makes up the border of a shape.
- Rectangle
- A flat shape with 4 sides where opposite sides are equal and all corners are square.
- Length
- How long one side of a shape is, measured in units like inches, feet, or centimeters.
- Formula
- A math shortcut written with numbers and symbols to solve a problem faster.
- Unit
- The measurement label you use, such as inches, feet, or centimeters.
Worked examples
A rectangle is 5 cm long and 3 cm wide. What is its perimeter?
→ 5 + 3 + 5 + 3 = 16 cm · Opposite sides of a rectangle are equal, so you add each length and width twice.
A rectangle is 5 cm long and 3 cm wide. What is its area?
→ 5 × 3 = 15 square cm · Multiplying length times width tells you how many square centimeters fit inside.
A square has sides that are each 4 inches long. What is its perimeter?
→ 4 + 4 + 4 + 4 = 16 inches · A square has 4 equal sides, so you can also multiply 4 × 4 = 16.
A square has sides that are each 4 inches long. What is its area?
→ 4 × 4 = 16 square inches · Even though the perimeter and area both equal 16 here, perimeter is in inches and area is in square inches — they measure different things.
A garden is shaped like a rectangle. It is 8 feet long and 2 feet wide. How much fencing is needed to go around it?
→ 8 + 2 + 8 + 2 = 20 feet of fencing · Fencing goes around the outside, so you need the perimeter.
A classroom floor is 9 meters long and 6 meters wide. How many square meters of carpet are needed to cover it?
→ 9 × 6 = 54 square meters · Covering a floor means filling the inside space, so you need the area.
Common mistakes
- Mixing up area and perimeter — remember, perimeter is the path around the outside, area is the space on the inside.
- Forgetting to write square units for area — area is always in square units (like square cm), not just cm.
- Only adding two sides for perimeter instead of all four sides of a rectangle.
- Multiplying all four sides together instead of adding them when finding perimeter.
- Forgetting that opposite sides of a rectangle are equal, and using the wrong number for a missing side.
FAQs
How do I remember which is area and which is perimeter?
Think of perimeter as the 'rim' or edge going all the way around — the word perimeter even has the word 'rim' hiding in it. Area is the space inside, like the area of a room.
Do I always multiply to find area?
For rectangles and squares, yes — multiply length times width. In 3rd grade, most area problems use rectangles and squares, so multiplying is the go-to method.
Why does area use square units but perimeter does not?
Perimeter is just a length — a line going around the shape — so it uses regular units like inches or cm. Area covers a flat surface, and you are counting squares, so it uses square units like square inches.
What if a shape is not a rectangle? How do I find the perimeter?
For any shape, just add up the lengths of all the sides. For example, a triangle with sides of 3 cm, 4 cm, and 5 cm has a perimeter of 3 + 4 + 5 = 12 cm.
Can two shapes have the same perimeter but different areas?
Yes! A rectangle that is 1 cm by 5 cm has a perimeter of 12 cm and area of 5 square cm. A rectangle that is 3 cm by 3 cm also has a perimeter of 12 cm but an area of 9 square cm. Same perimeter, different area.
My child keeps getting area and perimeter mixed up on tests. Any tips?
Practice connecting each to a real-life job: perimeter is for fencing a yard or putting a border on a picture frame (going around), and area is for buying carpet or painting a wall (covering the inside). Drawing a shape and labeling the outside versus inside can also help.
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