Area, Perimeter and Volume

This lesson covers DfE content statements L1.22, L1.23 and L1.24 — calculating perimeters and areas of rectangles and composite shapes made from rectangles; calculating volumes of cubes and cuboids; recognising common 2-D shapes; understanding line symmetry; and measuring angles.

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Perimeter

The perimeter is the total distance around the outside of a shape. Think of it as the length of fence you would need to go all the way around a garden.

Perimeter of a Rectangle

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

Perimeter = l + w + l + w = 2 × (l + w)

Worked Example — Garden Fencing

Scenario: A rectangular garden is 12 m long and 8 m wide. How much fencing is needed to go around it?

Perimeter = 2 × (12 + 8) = 2 × 20 = 40 m

Perimeter of Composite Shapes

A composite shape is made from two or more rectangles joined together (like an L-shape or T-shape). To find the perimeter, add up all the outside edges.

Worked Example — L-Shaped Room

Scenario: An L-shaped office has overall dimensions of 10 m by 8 m, with a 4 m × 3 m rectangle cut from one corner.

Step 1: Find the missing side lengths.

Side	How to find it	Length
Top	Given	10 m
Right (upper section)	8 − 3 = 5	5 m
Step across (going left)	Given	4 m
Step down	Given	3 m
Bottom	10 − 4 = 6	6 m
Left	Given	8 m

Step 2: Add all the sides.

Perimeter = 10 + 5 + 4 + 3 + 6 + 8 = 36 m

Exam Tip: For composite shapes, label every side length on the diagram before you start adding. Find missing lengths by subtracting from the overall dimensions. Tick off each side as you add it.

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Area

Area is the amount of surface a shape covers, measured in square units (cm², m², etc.).

Area of a Rectangle

Area = length × width

Worked Example — Carpet

Scenario: A bedroom is 5 m long and 4 m wide. How much carpet is needed?

Area = 5 × 4 = 20 m²

Worked Example — Cost of Flooring

Scenario: A kitchen is 6 m by 3.5 m. Floor tiles cost £15 per m². What is the total cost?

Step 1: Area = 6 × 3.5 = 21 m² Step 2: Cost = 21 × £15 = £315

Area of Composite Shapes (L-Shapes)

To find the area of a composite shape, split it into rectangles, find the area of each, and add them together.

Worked Example — L-Shaped Garden

Scenario: A garden is shaped like an L. It can be split into two rectangles:

    ┌────────────────┐
    │   Rectangle A  │ 3 m
    │   8 m × 3 m    │
    ├────────┐       │
    │        │       │
    │ Rect B │       │
    │ 4 m×5m │       │
    │        │       │
    └────────┘       │
         4 m    4 m

Wait — let me use a clean calculation:

Rectangle A: 8 m × 3 m = 24 m² Rectangle B: 4 m × 5 m = 20 m² Total area: 24 + 20 = 44 m²

Alternative method: You can also find the area of the full outer rectangle and subtract the "missing" rectangle.

Full rectangle: 8 m × 8 m = 64 m² Missing piece: 4 m × 5 m = 20 m² Area = 64 − 20 = 44 m² ✓ Same answer.

Worked Example — Painting a Wall

Scenario: A rectangular wall is 4 m wide and 2.5 m high. It has a window that is 1.2 m wide and 1 m high. How much wall area needs painting?

Step 1: Wall area = 4 × 2.5 = 10 m² Step 2: Window area = 1.2 × 1 = 1.2 m² Step 3: Area to paint = 10 − 1.2 = 8.8 m²

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Volume

Volume is the amount of space a 3-D shape takes up, measured in cubic units (cm³, m³, etc.).

At Level 1, you need volume of cubes and cuboids only.

Volume of a Cuboid

A cuboid has three measurements: length, width and height.

Volume = length × width × height