Perimeter And Area — 3–5 Math | Scholars & Parents

What Is This?

Perimeter is the total distance around the outside of a shape — the sum of all its side lengths. Area is the amount of space inside a shape — measured in square units. Both are measurements of flat (2D) shapes, but they measure completely different things.

Why Does It Matter?

Perimeter and area appear constantly in real life. Fencing a garden uses perimeter. Carpeting a room uses area. Wrapping a gift uses area. Running a lap around a track uses perimeter. Understanding both — and knowing which one to use — is one of the most practical skills in all of mathematics.

Perimeter

What Is Perimeter?

Perimeter is the distance you would travel if you walked all the way around the outside edge of a shape. You find it by adding all the side lengths together.

Formula for any shape:

Perimeter = sum of all sides

Perimeter of a Rectangle

A rectangle has two pairs of equal sides: length (l) and width (w).

P = 2 × (l + w) or equivalently P = 2l + 2w

Example: A rectangle with length 8 cm and width 5 cm.

P = 2 × (8 + 5) = 2 × 13 = 26 cm ✓

Perimeter of a Square

All four sides of a square are equal (side length s).

P = 4 × s

Example: A square with side 7 m.

P = 4 × 7 = 28 m ✓

Perimeter of Other Shapes

Add all the side lengths.

Example: A triangle with sides 5 cm, 8 cm, and 6 cm.

P = 5 + 8 + 6 = 19 cm ✓

Example: An L-shaped room with sides 10, 6, 4, 3, 6, 3 m.

P = 10 + 6 + 4 + 3 + 6 + 3 = 32 m ✓

Area

What Is Area?

Area is the amount of flat space a shape covers. It is measured in square units: cm², m², km², in², ft², etc.

Think of covering a floor with square tiles — the number of tiles needed is the area.

Area of a Rectangle

A = l × w

Example: A rectangle 8 cm long and 5 cm wide.

A = 8 × 5 = 40 cm² ✓

Area of a Square

A = s × s = s²

Example: A square with side 7 m.

A = 7 × 7 = 49 m² ✓

Area by Counting Squares

For irregular or drawn shapes, you can count the unit squares inside. Each whole square = 1 square unit. Half squares can be combined.

Perimeter vs Area — Key Differences

	Perimeter	Area
What it measures	Distance around the outside	Space inside
Unit	cm, m, km (linear)	cm², m², km² (square)
Rectangle formula	2 × (l + w)	l × w
Square formula	4 × s	s × s

⚠️ A common mistake is using the wrong formula. Always ask: am I finding the edge (perimeter) or the inside space (area)?

Finding a Missing Side

If you know the perimeter and one side, you can work backwards to find a missing side.

Example: A rectangle has perimeter 28 cm and length 9 cm. What is the width?

P = 2 × (l + w)
28 = 2 × (9 + w)
14 = 9 + w
w = 5 cm ✓

Example: A square has perimeter 36 m. What is the side length?

P = 4 × s
36 = 4 × s
s = 9 m ✓

Compound Shapes

A compound shape (also called a composite shape) is made up of two or more rectangles joined together. To find its area, split it into rectangles, find each area, and add them together.

Example: An L-shaped room.

+--------+
|        |
|   A    +----+
|        | B  |
+--------+----+

Measure rectangle A and rectangle B separately.
Area = Area A + Area B

For perimeter of a compound shape, add only the outer edges — do not include any interior lines.

Worked Examples

Worked Example 1: Rectangle, 12 m × 4 m

Perimeter: 2 × (12 + 4) = 2 × 16 = 32 m
Area: 12 × 4 = 48 m²

Worked Example 2: Square, side 9 cm

Perimeter: 4 × 9 = 36 cm
Area: 9 × 9 = 81 cm²

Worked Example 3: Find width when P = 30 m, l = 9 m

30 = 2 × (9 + w) → 15 = 9 + w → w = 6 m

Worked Example 4: Compound shape

Shape is 10 m × 6 m with a 4 m × 3 m rectangle removed from one corner.
Full rectangle area: 10 × 6 = 60 m²
Removed piece: 4 × 3 = 12 m²
Remaining area: 60 − 12 = 48 m²

Worked Example 5 (Word Problem):

A school field is 45 m long and 30 m wide. The school wants to put a fence around it. How many metres of fencing are needed?

This asks for perimeter (distance around).
P = 2 × (45 + 30) = 2 × 75 = 150 m of fencing ✓

Common Mistakes

Mistake 1: Confusing perimeter and area "How much carpet is needed?" → area. "How much skirting board is needed?" → perimeter. Read carefully.

Mistake 2: Using the wrong units Perimeter is in linear units (cm, m). Area is in square units (cm², m²). Never write cm for area or cm² for perimeter.

Mistake 3: Only multiplying two sides for perimeter P = l + w is only half the rectangle. The correct formula is P = 2 × (l + w).

Mistake 4: Forgetting missing sides in compound shapes When finding the perimeter of an L-shape, you must work out any unlabelled sides using the given measurements before adding them up.

Key Takeaways

Perimeter = sum of all outer sides; for rectangles: P = 2 × (l + w); for squares: P = 4 × s
Area = space inside a shape; for rectangles: A = l × w; for squares: A = s²
Perimeter uses linear units; area uses square units (²)
To find a missing side: rearrange the perimeter formula
For compound shapes: split into rectangles, find each area, then add (or subtract)
Always check which measurement the problem is asking for before calculating

Practice and Resources

Ready to practise? Try our Grade 3-5 Perimeter and Area Worksheet with problems on rectangles, squares, missing sides, and compound shapes. Test yourself with the Grade 3-5 Math Practice Test.