Word problems with perimeter and area

Word problems with perimeter and area

Word problems with perimeter and area

The hardest part of geometry word problems isn't the multiplication — it's deciding whether to use perimeter or area. A quick rule:

  • Perimeter for anything that runs around a shape: fences, ribbons, picture frames, border tiles.
  • Area for anything that covers a surface: paint, carpet, lawn, paper, glass.

Formulae you'll need

For a rectangle of length L and width W:

Perimeter = 2 × (L + W) = 2L + 2W

Area = L × W

For a square with side S:

Perimeter = 4 × S

Area = S × S

Worked examples

Example 1 — perimeter (fence around a garden)

A rectangular garden is 8 m long and 5 m wide. The owner wants to put a fence all the way around. How many meters of fence are needed?

Perimeter = 2 × (8 + 5) = 2 × 13 = 26 m.

Example 2 — area (paint on a wall)

A wall is 4 m wide and 3 m tall. A 1-litre tin of paint covers 6 m². How many tins do you need?

Area = 4 × 3 = 12 m².

Tins needed = 12 ÷ 6 = 2 tins.

Example 3 — combining both

A rectangular swimming pool is 20 m by 10 m. A 1-meter-wide concrete path goes all the way around it. What's the area of the concrete path?

Two ways:

  • Outer rectangle is (20 + 2) × (10 + 2) = 22 × 12 = 264 m².
  • Inner rectangle (the pool) is 20 × 10 = 200 m².
  • Path = 264 − 200 = 64 m².

Example 4 — finding a missing side

A rectangular room has an area of 48 m² and a length of 8 m. How wide is it?

If L × W = 48 and L = 8, then W = 48 ÷ 8 = 6 m.

Example 5 — fitting tiles

A bathroom floor is 3 m by 2 m. Square tiles measure 20 cm on each side. How many tiles do you need?

Convert units first: 3 m = 300 cm, 2 m = 200 cm.

Tiles along the length: 300 ÷ 20 = 15.

Tiles along the width: 200 ÷ 20 = 10.

Total tiles = 15 × 10 = 150 tiles.

Watch your units

This is where most mistakes happen.

  • Length: cm, m, km.
  • Area: cm², m², km² (a square unit, never just "m").
  • Always check the answer's unit makes sense: a garden's perimeter shouldn't be in m², and its area shouldn't be in m.

A room is 4 m × 3 m. What's its area?

Answer: 12 m² — the little 2 is essential.

Common pitfalls

Mixing perimeter and area in the same problem

Read carefully: "around" vs "covers" tells you which one to use.

Using mixed units

If one side is in meters and the other in centimeters, convert first. Don't compute 3 × 50 = 150 unless you know whether that's 150 cm² or 150 m·cm (nonsense).

Forgetting the dimensions of compound shapes

If a shape has an L-shape or a step, split it into rectangles and add their areas. Don't try to apply L × W to the whole thing in one go.

Practice