Choose a measurement before choosing a formula: perimeter is a boundary length, area is surface covered and volume is space occupied.
Foundation and Higher · Useful for students building fluency and applying the method in GCSE questions.
Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.
Higher extension. No questions in this selected set are labelled Higher extension. These core methods also support Higher revision.
3 worked examples and 8 original practice questions · Allow 25–40 minutes · Read online or print. Higher extensions are labelled. No account or email needed.
Printing includes the method, examples and space for working, followed by a separate answer section.
An internal dividing line is not part of the outside perimeter. Multiplying every given length is not a general volume method.
Read each line of working and explain why it follows from the previous line.
Perimeter adds lengths around the outside. Area measures the surface inside; choose a formula using the perpendicular dimensions.
Area and Perimeter · Core GCSE skill · Calculator allowed · 2 marks
A rectangle has length 9 cm and width 4 cm.
Now practise this method: Question 1 · Question 2 · Question 3
Split into familiar shapes and add non-overlapping areas, or subtract a removed region. Count any overlap only once.
Area of Compound Shapes · Core GCSE skill · Calculator allowed · 3 marks
A rectangle is 12 cm long and 9 cm wide.
A rectangle 5 cm by 4 cm is removed from one corner.
Work out the area of the remaining shape.
Given diagram. A rectangle is 12 cm long and 9 cm wide. A rectangle 5 cm by 4 cm is removed from one corner. Work out the area of the remaining shape. Use the labelled information; do not estimate measurements from the sketch.
Now practise this method: Question 4 · Question 5
Find the area of the constant cross-section, then multiply by the prism length. Area uses square units; volume uses cubic units.
Volume of a Prism · Core GCSE skill · Calculator allowed · 3 marks
The cross-section of a prism is a right-angled triangle with base 8 cm and height 5 cm.
The length of the prism is 12 cm.
Work out the volume of the prism.
Given diagram. The cross-section of a prism is a right-angled triangle with base 8 cm and height 5 cm. The length of the prism is 12 cm. Work out the volume of the prism. Use the labelled information; do not estimate measurements from the sketch.
Now practise this method: Question 6 · Question 7 · Question 8
Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.
Area and Perimeter · Core GCSE skill · No calculator · 2 marks
A triangle has base 12 cm and perpendicular height 5 cm.
Work out the area of the triangle.
Area and Perimeter · Core GCSE skill · Calculator allowed · 2 marks
Ben wants to work out the perimeter of a square with sides of length 6 cm.
Ben writes:
perimeter = 6 × 6 = 36 cm
Explain the mistake Ben has made.
Area and Perimeter · Core GCSE skill · No calculator · 3 marks
An L-shape is made by removing a rectangle 3 cm by 2 cm from one corner of a rectangle 8 cm by 6 cm.
Work out the perimeter of the L-shape.
Given diagram. An L-shape is made by removing a rectangle 3 cm by 2 cm from one corner of a rectangle 8 cm by 6 cm. Work out the perimeter of the L-shape. Use the labelled information; do not estimate measurements from the sketch.
Area of Compound Shapes · Core GCSE skill · No calculator · 2 marks
An L-shape is made by joining a rectangle 8 cm by 5 cm to a rectangle 4 cm by 3 cm. The two rectangles do not overlap.
Work out the total area of the L-shape.
Given diagram. An L-shape is made by joining a rectangle 8 cm by 5 cm to a rectangle 4 cm by 3 cm. The two rectangles do not overlap. Work out the total area of the L-shape. Use the labelled information; do not estimate measurements from the sketch.
Area of Compound Shapes · Core GCSE skill · Calculator allowed · 4 marks
The front of a shed is made from a rectangle with a triangle on top.
The rectangle is 10 cm wide and 6 cm high in a scale drawing. The triangle sits exactly on top of the rectangle, with base 10 cm and perpendicular height 4 cm.
Work out the total area of the scale drawing.
Given diagram. The front of a shed is made from a rectangle with a triangle on top. The rectangle is 10 cm wide and 6 cm high in a scale drawing. The triangle sits exactly on top of the rectangle, with base 10 cm and perpendicular height 4 cm. Work out the total area of the scale drawing. Use the labelled information; do not estimate measurements from the sketch.
Volume of a Prism · Core GCSE skill · No calculator · 2 marks
A cuboid measures 6 cm by 4 cm by 3 cm.
Work out the volume of the cuboid.
State the units of your answer.
Volume of a Prism · Core GCSE skill · No calculator · 3 marks
A cuboid has a volume of 180 cm3.
The base of the cuboid measures 6 cm by 5 cm.
Work out the height of the cuboid.
Volume of a Prism · Core GCSE skill · Calculator allowed · 3 marks
The cross-section of a prism is a trapezium.
The parallel sides of the trapezium are 6 cm and 10 cm, and the perpendicular distance between them is 4 cm.
The length of the prism is 15 cm.
Work out the volume of the prism.
Given diagram. The cross-section of a prism is a trapezium. The parallel sides of the trapezium are 6 cm and 10 cm, and the perpendicular distance between them is 4 cm. The length of the prism is 15 cm. Work out the volume of the prism. Use the labelled information; do not estimate measurements from the sketch.
Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.
Workouts provide interactive practice; choose the tier your school has recommended.
Give students time to write the method, then compare their working with the answer section. Ask which step they would check first if their answer differs.
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