Perimeter, Area and Volume
Perimeter, Area and Volume is the Year 5 topic covering finding the perimeter of rectilinear shapes by adding the lengths of all the sides, finding the area of a rectangle by multiplying its length by its width, and finding the volume of a cuboid by multiplying length by width by height.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find the perimeter of any rectilinear shape, add together the lengths of all its sides, making sure every side is included and in the same unit.
- For a composite shape with a missing side length, use the fact that opposite outer edges must add up to the same total to work out the missing length before adding all the sides.
- To find the area of a rectangle, multiply its length by its width; always give the answer in square units, e.g. sq cm or sq m.
- To find the area of a composite rectilinear shape, split it into two or more rectangles, find the area of each rectangle separately, then add the areas together.
- To find the volume of a cuboid, multiply its length by its width by its height; the answer is given in cubic units, e.g. cu cm.
- Keep units consistent throughout a calculation: convert every measurement to the same unit (e.g. all in cm) before working out a perimeter, area or volume.
- Sketch and label a composite shape if one is not already labelled, marking on any missing lengths you calculate, to avoid missing or double-counting a side.
Worked example
An L-shaped room is made from a large rectangle 8 m by 5 m with a smaller rectangle 3 m by 2 m cut out of one corner. Find the area of the L-shaped room.
- Find the area of the large rectangle as if no corner were missing: 8 x 5 = 40 sq m.
- Find the area of the small rectangle that has been cut out of the corner: 3 x 2 = 6 sq m.
- Subtract the cut-out area from the large rectangle's area: 40 - 6 = 34.
- So the area of the L-shaped room is 34 sq m.
Practice questions
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Q1A rectangular field is 60 m long and 25 m wide. Find its perimeter.Show answer
Answer: 170 m (2 x (60 + 25) = 2 x 85 = 170)
Q2A rectangular playground is 40 m long and 18 m wide. Find its area.Show answer
Answer: 720 sq m (40 x 18)
Q3A square patio has sides of 6 m. Find its perimeter and its area.Show answer
Answer: Perimeter 24 m (4 x 6); area 36 sq m (6 x 6)
Q4A cuboid box measures 5 cm by 4 cm by 3 cm. Find its volume.Show answer
Answer: 60 cu cm (5 x 4 x 3)
Q5A rectangle has an area of 48 sq cm and a length of 8 cm. Find its width.Show answer
Answer: 6 cm (48 / 8)
Q6A composite shape is made from a rectangle 10 cm by 6 cm with a rectangle 4 cm by 3 cm attached to one side. Find the total area.Show answer
Answer: 72 sq cm (10 x 6 = 60, plus 4 x 3 = 12, total 60 + 12 = 72)
Q7A cube-shaped storage box has sides of 7 cm. Find its volume.Show answer
Answer: 343 cu cm (7 x 7 x 7)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
An L-shaped garden is made from a large rectangle 12 m long and 9 m wide, with a smaller rectangular corner of length 5 m and width 4 m cut away from one corner. (a) Find the two missing side lengths needed to work out the perimeter: the remaining part of the long side, and the remaining part of the width. (2 marks) (b) Find the total area of the garden. (2 marks)
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A cuboid-shaped fish tank measures 40 cm long, 25 cm wide and 30 cm tall. (a) Find the volume of the tank. (2 marks) (b) The tank is filled with water to a depth of 18 cm. Find the volume of water in the tank. (2 marks)
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A rectangle has a perimeter of 36 cm and a width of 7 cm. Find its length.
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Nothing ticked yet - 2 available
Free printable worksheet
Want more practice on paper? Download the perimeter, area and volume 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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