Perimeter and Area
Grade 4 · Math · Study Guide
Learn how to find the perimeter and area of rectangles and other shapes.
Perimeter and area both describe measurements of shapes, but they measure very different things. Perimeter is the total distance around the outside of a shape — like a fence around a yard. Area is the amount of space inside the shape — like the grass inside that fence.
To find the perimeter of any shape, add up all the side lengths. For a rectangle with length 8 cm and width 5 cm, the perimeter is 8 + 5 + 8 + 5 = 26 cm. You can also use the formula P = 2 × (l + w) = 2 × (8 + 5) = 2 × 13 = 26 cm.
Area tells you how many unit squares fit inside a shape. For rectangles, the formula is A = length × width. A rectangle that is 8 cm long and 5 cm wide has an area of 8 × 5 = 40 square centimeters. We write area in square units (cm², ft², in²).
A great way to remember the difference: perimeter uses linear units (cm, m, ft) while area always uses SQUARE units (cm², m², ft²). If someone asks you to tile a floor, they want area. If they want to put a border around a picture frame, they want perimeter.
| Length | Width | Perimeter | Area |
|---|---|---|---|
| 6 cm | 4 cm | 20 cm | 24 cm² |
| 10 m | 3 m | 26 m | 30 m² |
| 7 ft | 7 ft | 28 ft | 49 ft² |
| 12 in | 5 in | 34 in | 60 in² |
Key terms
- Perimeter
- The total distance around the outside of a shape.
- Area
- The number of square units needed to cover the inside of a shape.
- Square units
- The unit used to measure area, like cm² or ft².
- Formula
- A math rule expressed with symbols that you use to calculate something.
Flashcards
- Perimeter formula (rectangle)
- P = 2 × (length + width)
- Area formula (rectangle)
- A = length × width
- Perimeter units
- Linear units: cm, m, ft, in
- Area units
- Square units: cm², m², ft², in²
- Perimeter of a 6×4 rectangle
- 2 × (6+4) = 20 units
- Area of a 6×4 rectangle
- 6 × 4 = 24 square units
Practice questions
What is the perimeter of a rectangle with length 9 cm and width 4 cm?
- 13 cm
- 26 cm
- 36 cm
- 72 cm
Show answer
Answer: 26 cm
P = 2 × (9 + 4) = 2 × 13 = 26 cm.
Area is measured in square units.
Show answer
Answer: True
Area measures the space inside a shape, so it is always expressed in square units.
The area of a rectangle with length 7 ft and width 5 ft is ___ ft².
Show answer
Answer: 35
A = 7 × 5 = 35 square feet.
A square has sides of 6 inches each. What is its area?
- 12 in²
- 24 in²
- 36 in²
- 48 in²
Show answer
Answer: 36 in²
A square with side 6: A = 6 × 6 = 36 in².
The perimeter formula for a rectangle is P = 2 × (l + ___).
Show answer
Answer: w
The perimeter formula for a rectangle is P = 2 × (l + w), where l is length and w is width.
Fun facts
- Two shapes can have the same perimeter but very different areas! A 1×9 rectangle and a 3×3 square both have perimeter 20, but areas of 9 and 9 — wait, actually 9 vs 9. Try a 1×9 (area 9) vs 5×5 (area 25, perimeter 20). Same perimeter, wildly different areas!
- Architects calculate area to plan how many people can safely be in a room and how much flooring material to buy.
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