Perimeter and Area
Perimeter and Area is the Year 4 topic covering measuring and calculating the perimeter of rectilinear shapes, those made only of straight sides meeting at right angles, and finding area by counting squares on a grid; perimeter is the distance around a shape's edge and area is the surface it covers.
Before you start
Make sure you're comfortable with these topics first:
Method
- For perimeter, identify the length of every side of the shape, then add all the side lengths together.
- For a rectangle, use the shortcut: perimeter = (length + width) x 2, since opposite sides are equal.
- For an L-shape or another rectilinear shape, work out any missing side lengths first, using the fact that the shape's total width and height in each direction must match up, then add every side.
- For area by counting squares, count every whole square inside the shape on a squared grid, and combine part-squares (such as two half-squares) to make whole squares.
- For a rectangle drawn on a grid, count the squares along one side and the squares along the other side, then multiply them: this gives the same answer as counting every square, but faster.
- Always give the correct units: perimeter is measured in a length unit (cm, m); area is measured in a squared unit (cm2, m2).
Worked example
A rectangular football pitch marking is 12 m long and 7 m wide. Work out its perimeter, and work out its area.
- Perimeter = (length + width) x 2 = (12 + 7) x 2.
- 12 + 7 = 19, so the perimeter = 19 x 2 = 38 m.
- Area = length x width = 12 x 7.
- 12 x 7 = 84, so the area is 84 m2.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A rectangle is 9 cm long and 4 cm wide. Work out its perimeter.Show answer
Answer: 26 cm, because (9 + 4) x 2 = 26
Q2A square field has sides of 15 m. Work out its perimeter.Show answer
Answer: 60 m (15 x 4)
Q3A rectangle measures 6 cm by 5 cm. Work out its area.Show answer
Answer: 30 cm2 (6 x 5)
Q4A rectangular rug is 3 m long and 2 m wide. What is its area?Show answer
Answer: 6 m2 (3 x 2)
Q5An L-shaped room is made from a 5 m by 4 m rectangle with a 2 m by 2 m square cut out of one corner. Does cutting out the corner change the total perimeter of the room? Explain your answer.Show answer
Answer: No, the perimeter stays the same. The original rectangle's perimeter is (5 + 4) x 2 = 18 m. Cutting out the 2 m by 2 m corner removes two edges of 2 m each (4 m in total) but adds two new edges of 2 m each around the notch (4 m in total), so the perimeter is still 18 m, even though the area is now smaller.
Q6A square has an area of 49 cm2. What is the length of one side?Show answer
Answer: 7 cm, because 7 x 7 = 49
Q7Tariq is putting ribbon around a rectangular picture frame that is 24 cm long and 18 cm wide. How many centimetres of ribbon does he need?Show answer
Answer: 84 cm, because (24 + 18) x 2 = 84
Q8A rectangular classroom carpet covers an area of 12 m2. If the carpet is 4 m long, how wide is it?Show answer
Answer: 3 m, because 12 divided by 4 = 3
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A rectangular garden is 11 m long and 6 m wide. Work out the perimeter of the garden.
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A rectangular lawn measures 8 m by 5 m. A rectangular patio measuring 3 m by 2 m is built in one corner of the lawn. Work out the area of grass that is left. Show your working.
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A square has a perimeter of 32 cm. Circle the length of one of its sides: 4 cm, 8 cm, 16 cm.
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Free printable worksheet
Want more practice on paper? Download the perimeter and area worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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