A friendly flat-vector scene of labelled rectangles, a square and a composite L-shape on a warm off-white background in IllumiTutor navy and amber.

P4 Composite Area and Perimeter

Work backwards from area or perimeter, then split an L-shape without counting its internal divider.

⏱ 6 min · 🎯 3 things to master

Area counts the square units inside a shape. Perimeter traces the outside boundary. When a shape is made from rectangles and squares, split it into parts for area and trace only exposed outside edges for perimeter.

Parents: ask your child to name the unit before calculating. A square centimetre measures area; a centimetre measures a boundary length.

By the end you will be able to recover missing rectangle and square sides and find both area and perimeter of a composite L-shape.

Recover a missing rectangle side

For a rectangle, area = length × width and perimeter = 2 × (length + width).

🤔 Predict first: A rectangle has area 72 cm² and length 9 cm. What is its width?

Show the worked solution

Rectangle missing sides

72  cm2÷9  cm=8  cm72\,\text{ cm}^2\div9\,\text{ cm}=8\,\text{ cm}

The area check is 9 × 8 = 72 cm².

Rectangle missing sides

34  cm=2×(10  cm+w)34\,\text{ cm}=2\times(10\,\text{ cm}+w)
17  cm=10  cm+w⇒w=7  cm17\,\text{ cm}=10\,\text{ cm}+w\Rightarrow w=7\,\text{ cm}

The perimeter check is 2 × (10 + 7) = 34 cm.

Recover a square side

A square has area side × side and perimeter 4 × side. If the area is 81 cm², recognise 9 × 9 = 81, so the side is 9 cm. If the perimeter is 36 cm, divide 36 by 4 to get 9 cm.

Square missing sides

9×9=81  cm2⇒side=9  cm9\times9=81\,\text{ cm}^2\Rightarrow\text{side}=9\,\text{ cm}
36  cm÷4=9  cm36\,\text{ cm}\div4=9\,\text{ cm}

🤔 Predict first: A square has perimeter 36 cm. What is one side?

The L-shape: two area methods

Use the L-shape with outer width 8 cm, outer height 6 cm and a top-right cut-out 3 cm by 2 cm. Its six exposed boundary lengths, in order, are 8 cm, 4 cm, 3 cm, 2 cm, 5 cm and 6 cm.

Area and perimeter grid lab

Predict first: A rectangle is 9 cm by 8 cm. What is its area?

Subtraction: begin with the outer rectangle and remove the cut-out: 8 × 6 = 48 cm²; 3 × 2 = 6 cm²; 48 − 6 = 42 cm².

Addition: split into the left rectangle and lower-right rectangle: 5 × 6 = 30 cm² and 3 × 4 = 12 cm²; 30 + 12 = 42 cm².

The two methods agree because they cover the same L-shape.

Two area methods and the boundary

8×6−3×2=48−6=42  cm28\times6-3\times2=48-6=42\,\text{ cm}^2
5×6+3×4=30+12=42  cm25\times6+3\times4=30+12=42\,\text{ cm}^2
8+4+3+2+5+6=28  cm8+4+3+2+5+6=28\,\text{ cm}

For perimeter, follow the six outside segments. The line where the two addition rectangles touch is an internal divider, so it is not part of the perimeter.

Text alternative: the L-shape vertices are described by the six outside lengths above; the cut-out is 3 cm by 2 cm at the top right. No result depends on judging an unlabelled drawing.

Practise with worked steps

Practice givens 1: A rectangle has area 72 cm² and length 9 cm. Find its width.

Reveal solution: Practice 1

Given area 72 cm² and length 9 cm, width = 72 ÷ 9 = 8 cm. Check: 9 × 8 = 72 cm².

Find the width

72  cm2÷9  cm=8  cm72\,\text{ cm}^2\div9\,\text{ cm}=8\,\text{ cm}
9×8=72  cm29\times8=72\,\text{ cm}^2

Practice givens 2: A square has perimeter 36 cm. Find one side.

Reveal solution: Practice 2

Given perimeter 36 cm, side = 36 ÷ 4 = 9 cm. Check: 4 × 9 = 36 cm.

Find the square side

36  cm÷4=9  cm36\,\text{ cm}\div4=9\,\text{ cm}
4×9=36  cm4\times9=36\,\text{ cm}

Practice givens 3: An L-shape is an 8 cm by 6 cm rectangle with a top-right cut-out 3 cm by 2 cm. Find its area and exposed perimeter.

Reveal solution: Practice 3

Given outer rectangle 8 cm by 6 cm and cut-out 3 cm by 2 cm, area = 8 × 6 − 3 × 2 = 42 cm². The exposed boundary is 8 + 4 + 3 + 2 + 5 + 6 = 28 cm; do not add the shared internal divider.

Solve the composite

8×6−3×2=42  cm28\times6-3\times2=42\,\text{ cm}^2
8+4+3+2+5+6=28  cm8+4+3+2+5+6=28\,\text{ cm}
shared divider is internal\text{shared divider is internal}

Watch out

Quick recap

🎯 Mastery check

Answer all 7 — your progress is saved on this device.

  1. A rectangle has area 72 cm² and length 9 cm. What is its width?

  2. A rectangle has perimeter 34 cm and length 10 cm. What is its width?

  3. A square has area 81 cm². What is one side?

  4. A square has perimeter 36 cm. What is one side?

  5. An L-shape is an 8 cm by 6 cm rectangle with a 3 cm by 2 cm cut-out. What is its area?

  6. The L-shape boundary lengths are 8, 4, 3, 2, 5 and 6 cm. What is its perimeter?

  7. When two rectangles are used to find an L-shape area, which line is excluded from perimeter?