Perimeter, Area and Volume: Practice Set 2
Perimeter, Area and Volume: Practice Set 2 is a second practice round for 11+ shape work, revisiting the perimeter and area of rectangles and triangles before pushing into compound shapes, missing-length problems and the volume of cuboids.
Method
- Find the perimeter of a shape by adding together the lengths of all of its sides, making sure every side is included even if its length is not directly labelled.
- Find the area of a rectangle by multiplying its length by its width, and the area of a triangle by multiplying its base by its height and dividing by 2.
- For a compound shape, split it into rectangles (and triangles, if needed), find the area of each part separately, then add or subtract the parts as the shape requires.
- When a side length is missing, use the fact that opposite sides of a rectangle are equal, or that a shape's smaller measurements must add up to a given total length.
- Find the volume of a cuboid by multiplying its length, width and height together, keeping every measurement in the same unit first.
- Check your answer's unit matches what has been asked for, remembering that area is measured in square units and volume in cubic units.
Worked example
A rectangular garden measures 9 m by 6 m. A square patio of side 3 m is built inside it. Calculate the area of the garden that is not covered by the patio.
- Find the area of the garden: 9 x 6 = 54 square metres.
- Find the area of the patio: 3 x 3 = 9 square metres.
- Subtract the patio's area from the garden's area: 54 - 9 = 45 square metres.
- Final answer: 45 square metres.
Practice questions
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Q1Find the perimeter of a rectangle measuring 7 cm by 4 cm.Show answer
Answer: 22 cm
Q2Find the area of a rectangle measuring 12 m by 5 m.Show answer
Answer: 60 square metres
Q3A triangle has a base of 10 cm and a height of 6 cm. Find its area.Show answer
Answer: 30 square cm
Q4A cuboid measures 4 cm by 3 cm by 5 cm. Find its volume.Show answer
Answer: 60 cubic cm
Q5An L-shaped room is made from a 6 m by 4 m rectangle with a 2 m by 3 m rectangle removed from one corner. Find the remaining area.Show answer
Answer: 18 square metres
Q6A square has a perimeter of 32 cm. Find the length of one side.Show answer
Answer: 8 cm
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A rectangle has a length of 15 cm and a perimeter of 46 cm. Calculate its width.
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A garden is made up of a rectangular lawn measuring 8 m by 5 m and a triangular flower bed attached to one side, with a base of 5 m and a height of 4 m. Calculate the total area of the garden.
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A cuboid-shaped water tank measures 80 cm long, 50 cm wide and 40 cm high. (a) Calculate the volume of the tank in cubic centimetres. (b) Given that 1000 cubic centimetres holds 1 litre, calculate the tank's capacity in litres.
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Free printable worksheet
Want more practice on paper? Download the perimeter, area and volume: practice set 2 worksheet pack - 12 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.
This topic is chapter 23 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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