Maths

Common mistakes in area and perimeter of rectangles

4 mistakes learners make with area and perimeter of rectangles, each one named and explained.

All common mistakes

Perimeter is the distance round the edge; area is the space inside.

Area given where perimeter was asked for

What it looks like

The two lengths are multiplied and given as the distance round the edge.

Why it happens

Multiplying is the move most practised in this topic, so it happens by reflex.

A worked example

Question. A garden 12 m by 5 m, fenced all round

A common answer. 12 x 5 = 60

The answer. 2 x (12 + 5) = 34

Why. The fence follows the edge, so the four sides are added.

Put the two side by side

Area fills the shape.
Perimeter traces its outline.

Trace the fence with your finger. You are adding lengths, never multiplying them.

One side used for both dimensions

What it looks like

A rectangle is treated as a square, so one of its sides is multiplied by itself.

Why it happens

Area is remembered as a side times a side, and which two sides is not part of the memory.

A worked example

Question. A rectangle 8 cm by 5 cm

A common answer. 8 x 8 = 64

The answer. 8 x 5 = 40

Why. The two sides of a rectangle are different, and the area uses one of each.

Put the two side by side

A square: side times the same side.
A rectangle: length times width, two different numbers.

Point at both measurements in the question. Both have to appear in the calculation.

The perimeter used as a side length

What it looks like

A square with perimeter 36 cm is treated as having sides of 36 cm.

Why it happens

The number given is the only length in the question, so it becomes the length used.

A worked example

Question. A square of perimeter 36 cm

A common answer. 36 x 36 = 1296 cm squared

The answer. 9 x 9 = 81 cm squared

Why. The 36 is spread across four equal sides, so each one is 9.

Put the two side by side

Perimeter 36 is the whole way round.
Each side is 36 divided by 4.

Before using a length, ask whether it is one side or all of them.

The sides added instead of multiplied

What it looks like

Area is given as length plus width.

Why it happens

Adding is the first operation you reach for, and it does use both numbers.

A worked example

Question. A rectangle 8 cm by 5 cm

A common answer. 8 + 5 = 13

The answer. 8 x 5 = 40

Why. Five rows of eight squares is a multiplication.

Put the two side by side

13 is smaller than one of the sides times two.
40 is how many unit squares fit inside.

Picture the squares. Counting them is always a multiplication.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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