Geometry: Area, Perimeter and Volume
Area, perimeter and volume covers calculating the space inside 2D shapes (area), the distance around them (perimeter), and the space inside 3D solids (volume), including rectangles, triangles, parallelograms, trapeziums, circles, prisms and cuboids. These skills use standard formulae plus circle facts involving pi, and appear throughout KS3 in real-life contexts such as flooring, paint and water capacity.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the shape and recall its area or volume formula (e.g. area of a triangle = 0.5 x base x height, volume of a cuboid = length x width x height).
- For compound or L-shapes, split the shape into simpler rectangles or triangles, or use a bounding shape and subtract the missing piece.
- For circles, use circumference = pi x diameter and area = pi x radius^2, substituting the given radius or diameter carefully.
- For prisms, find the area of the cross-section first, then multiply by the length of the prism to get the volume.
- Check that all lengths are in the same unit before calculating, converting where necessary (e.g. cm to m).
- Round your final answer to the accuracy asked for (such as 3 significant figures) and include the correct units.
Worked example
A circular pond has a radius of 4.5 m. Calculate its circumference, giving your answer to 3 significant figures.
- Circumference = pi x diameter, and diameter = 2 x radius = 2 x 4.5 = 9 m.
- Circumference = pi x 9.
- Using pi = 3.14159..., circumference = 28.274... m.
- Round to 3 significant figures: 28.3 m.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A triangular prism has a cross-section with base 6 cm and perpendicular height 5 cm. The prism is 10 cm long. Calculate the volume of the prism.
A wall measures 5 m long and 2.4 m high. It contains one window measuring 1.4 m by 1.2 m. One litre of paint covers 10 m^2, and paint is sold only in 2-litre tins. (a) Calculate the area of wall to be painted. (b) Calculate the minimum number of tins needed.
A cylindrical water tank has a diameter of 1.4 m and a height of 2 m. Calculate the volume of the tank in m^3, giving your answer to 3 significant figures.
Free printable worksheet
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