Geometry and Measures Depth
Geometry and Measures Depth brings together the main strands of primary geometry and measures, angles, properties of 2D shapes, perimeter, area, and unit conversion, in combined questions rather than testing each skill in isolation. 11+ papers often ask a single question that requires, for example, converting units before finding an area, or using an angle fact to find a missing side, so this set trains moving fluently between these related skills within one question.
Before you start
Make sure you're comfortable with these topics first:
Method
- Before calculating, identify every shape fact given, such as angle rules, side lengths or whether a shape is regular, and every measure given, noting its units.
- Convert all measurements to the same unit first, all in cm, or all in m, before doing any calculation involving more than one length.
- Recall the core angle facts: angles on a straight line sum to 180 degrees, angles around a point sum to 360 degrees, and angles in a triangle sum to 180 degrees.
- Recall the area and perimeter formulae for rectangles, area = length x width and perimeter = 2 x (length + width), and apply them to compound shapes by splitting the shape into rectangles.
- Sketch a quick diagram if one is not given, marking on it every length and angle from the question, since geometry problems are much easier to solve from a labelled picture.
- Check your final answer's unit matches what the question asked for, such as cm squared for an area or cm for a length, and that its size is realistic for the shape described.
Worked example
A rectangular garden is 5 m long and 300 cm wide. What is the area of the garden in square metres?
- Convert both measurements to the same unit: 300 cm = 3 m, so the garden is 5 m by 3 m.
- Use the area formula for a rectangle: area = length x width.
- Calculate: 5 x 3 = 15.
- The area of the garden is 15 square metres.
Practice questions
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Q1Three angles on a straight line are 55 degrees, 65 degrees and x. What is the value of x?Show answer
Answer: 60 degrees
Q2A square has a perimeter of 36 cm. What is the length of one side?Show answer
Answer: 9 cm
Q3A rectangle has an area of 48 cm squared and a width of 6 cm. What is its length?Show answer
Answer: 8 cm
Q4Convert 2.5 metres into centimetres.Show answer
Answer: 250 cm
Q5A triangle has angles of 90 degrees and 35 degrees. What is the third angle?Show answer
Answer: 55 degrees
Q6A rectangular field is 120 m by 80 m. What is its perimeter in metres?Show answer
Answer: 400 m
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A rectangular lawn measures 8 m by 6 m. A path 1 m wide is built all the way around the inside edge of the lawn, reducing the area of grass. What is the area of grass remaining, in square metres?
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Two angles around a point are 110 degrees and 145 degrees. A third angle, x, completes the full turn. What is the size of angle x, and is it acute, obtuse or reflex?
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Free printable worksheet
Want more practice on paper? Download the geometry and measures depth worksheet pack - 15 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 25 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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