Geometry and Measures Depth Set 2
Geometry and Measures Depth Set 2 continues to combine angle facts, shape properties, perimeter, area and unit conversion into single questions, moving on to compound shapes built from more than one rectangle, angle problems involving parallel lines, and problems where a measurement must be converted before an area or volume calculation can be completed. It follows on from Geometry and Measures Depth.
Method
- Read the whole question before writing anything, noting every angle fact, shape property and unit given, since a Depth question often mixes several types of information.
- When lines cross or run parallel, use angle facts such as vertically opposite angles are equal, and co-interior angles on parallel lines sum to 180 degrees, alongside the standard angle facts for a straight line, a point and a triangle.
- Split any compound shape into rectangles or triangles you recognise, working out any missing lengths from the measurements you are given before finding each individual area.
- Convert every length to the same unit before combining measurements from different parts of the question, working in the smallest unit given to avoid decimals where possible.
- Build up multi-step answers in a clear order, using the result of one step as the input to the next, and labelling each intermediate value so you do not lose track of it.
- Check that your final answer has a sensible size and the correct unit for what was asked, whether that is a length, an area or a volume.
Worked example
A garden is made from a rectangle 6 m long and 4 m wide, with a triangular flower bed added to one short end. The triangular bed has the same 4 m width as its base and a height of 3 m. Find the total area of the garden.
- Find the area of the rectangular part: 6 x 4 = 24 m^2.
- Find the area of the triangular part using base x height x 0.5: 0.5 x 4 x 3 = 6 m^2.
- Add the two areas together, since the triangle is attached to the rectangle: 24 + 6.
- The total area of the garden is 30 m^2.
Practice questions
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Q1Two angles lie on a straight line. One is 3 times the size of the other. Find both angles.Show answer
Answer: 45 degrees and 135 degrees (x + 3x = 180, so x = 45)
Q2A rectangular room is 4.5 m long and 320 cm wide. Find its area in square metres.Show answer
Answer: 14.4 m^2 (4.5 m x 3.2 m)
Q3A shape is made from two rectangles: one measuring 9 cm by 5 cm and another measuring 4 cm by 5 cm, joined along one 5 cm edge to form a longer rectangle. Find the perimeter of the combined shape.Show answer
Answer: 36 cm (the combined rectangle is 13 cm by 5 cm, so perimeter = 2 x (13 + 5))
Q4A cuboid has a square base of side 30 cm and a height of 0.5 m. Find its volume in cm^3.Show answer
Answer: 45,000 cm^3 (30 x 30 x 50)
Q5Two parallel lines are crossed by a third line. One angle formed is 118 degrees. Find the co-interior angle on the same side.Show answer
Answer: 62 degrees (co-interior angles on parallel lines sum to 180 degrees, so 180 - 118 = 62)
Q6A triangle has one angle of 90 degrees and another angle twice the size of the third. Find all three angles.Show answer
Answer: 90, 60 and 30 degrees (90 + x + 2x = 180, so x = 30)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A rectangular field measures 2.4 m by 150 cm. (a) Convert 150 cm to metres. (b) Calculate the area of the field in square metres.
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Two angles on a straight line are in the ratio 2:7. (a) Write an expression for each angle in terms of x, where the smaller angle is 2x. (b) Form and solve an equation to find x. (c) State the size of the larger angle.
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A swimming pool is being built in the shape of a cuboid with a rectangular base 8 m long and 500 cm wide, and a uniform depth of 150 cm. (a) Convert the width and the depth to metres. (b) Calculate the volume of the pool in cubic metres. (c) Given that 1 cubic metre holds 1000 litres, calculate how many litres of water are needed to fill the pool completely.
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Free printable worksheet
Want more practice on paper? Download the geometry and measures depth set 2 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 26 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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