Geometry and Shape: Practice Set 4
Geometry and Shape: Practice Set 4 is a mixed geometry practice set combining perimeter and area calculations, angle facts, properties of 2D shapes, and 3D shape or net recognition. It brings together several separate geometry skills into one timed section, which is how GL Assessment and CEM-style papers usually test shape work, so a student must recognise quickly which skill each question needs.
Before you start
Make sure you're comfortable with these topics first:
Method
- Sort questions by type as you read them (angle facts, perimeter or area, or 2D/3D shape recognition), since each type needs a different first step.
- For angle questions, identify which angle fact applies (angles on a straight line total 180 degrees, around a point total 360 degrees, in a triangle total 180 degrees, in a quadrilateral total 360 degrees) before calculating.
- For perimeter, add every outside edge length; for area, choose the correct formula for the shape (rectangle: length x width; triangle: half x base x height) and always give the correct units.
- For a compound shape, split it into simple rectangles or triangles first, find the area of each part, then combine them by adding or subtracting.
- For 3D shape or net questions, visualise folding the net or rotating the shape, or sketch it if there is time, rather than guessing.
- Mark any working directly on a diagram if one is given, since this is faster and safer than working from memory.
- Check that units are consistent throughout a question (for example, everything in centimetres) before giving a final numeric answer.
Worked example
An L-shaped garden is made from a large rectangle 10m long by 8m wide, with a smaller rectangle 4m long by 3m wide cut out of one corner. Find the area of the L-shaped garden.
- Find the area of the large rectangle: 10 x 8 = 80 m^2.
- Find the area of the cut-out rectangle: 4 x 3 = 12 m^2.
- Subtract the cut-out area from the large rectangle's area: 80 - 12 = 68 m^2.
- State the final answer with units: the L-shaped garden has an area of 68 m^2.
Practice questions
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Q1Find the perimeter of a rectangle 9cm long and 5cm wide.Show answer
Answer: 2 x (9 + 5) = 2 x 14 = 28cm.
Q2A triangle has a base of 12cm and a height of 7cm. Find its area.Show answer
Answer: 1/2 x 12 x 7 = 42 cm^2.
Q3Two angles on a straight line are in the ratio 2:3. Find the size of each angle.Show answer
Answer: 180 shared in the ratio 2:3 is 5 parts, so each part is 36. The angles are 72 and 108 degrees.
Q4How many faces does a triangular prism have?Show answer
Answer: 5 faces (2 triangular ends and 3 rectangular sides).
Q5A square has an area of 49 cm^2. Find its perimeter.Show answer
Answer: Side length = square root of 49 = 7cm. Perimeter = 4 x 7 = 28cm.
Q6The angles in a quadrilateral are 90, 90, 60 and x degrees. Find x.Show answer
Answer: The angles in a quadrilateral total 360. 90 + 90 + 60 = 240, so x = 360 - 240 = 120.
Q7A cube has an edge length of 4cm. Find its volume.Show answer
Answer: 4 x 4 x 4 = 64 cm^3.
Q8What 3D shape has 1 circular face, 1 vertex, and a curved surface?Show answer
Answer: A cone.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A rectangular lawn measures 15m by 9m. A circular flower bed of radius 3m is cut out of the lawn. Using the approximation pi = 3.14, calculate the remaining area of the lawn, giving your answer to the nearest whole square metre.
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A cuboid has length 6cm, width 4cm and height x cm. Its volume is 120 cm^3. (a) Find the height, x. (b) Find the cuboid's total surface area.
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Free printable worksheet
Want more practice on paper? Download the geometry and shape: practice set 4 worksheet pack - 19 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 29 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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