Measurement: Units, Perimeter, Area and Volume
Year 6 measurement brings together converting between standard metric units of length, mass and capacity, and calculating perimeter and area for compound rectilinear shapes, plus the area of triangles and parallelograms and the volume of cuboids.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the metric conversion facts by heart: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 litre = 1000 ml; to convert to a smaller unit multiply, to convert to a bigger unit divide.
- For the perimeter of a compound (L-shaped or irregular) rectilinear shape, work out any missing side lengths first, since opposite sides of a rectangle-based shape must balance, then add every outer side.
- For the area of a compound rectilinear shape, split it into two or more rectangles, work out each rectangle's area, length times width, then add or subtract the areas as needed.
- For the area of a triangle, use base x height / 2, making sure the height used is the perpendicular, right-angle, height, not a sloping side.
- For the area of a parallelogram, use base x height, again using the perpendicular height between the two parallel sides.
- For the volume of a cuboid, multiply length x width x height; all three measurements must be in the same unit before you multiply.
- Always give the correct unit for the answer: a length is in cm or m, an area is in cm squared or m squared, and a volume is in cm cubed or m cubed.
- If a question mixes units, for example some lengths in cm and one in mm, convert everything to the same unit before doing any calculation.
Worked example
A triangle has a base of 12 cm and a perpendicular height of 7 cm. Find its area. Then find the volume of a cuboid box that is 12 cm long, 7 cm wide and 4 cm high.
- Area of a triangle = base x height / 2 = 12 x 7 / 2.
- 12 x 7 = 84.
- 84 / 2 = 42, so the triangle's area is 42 square cm.
- Volume of a cuboid = length x width x height = 12 x 7 x 4.
- 12 x 7 = 84, then 84 x 4 = 336, so the cuboid's volume is 336 cubic cm.
Practice questions
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Q1Convert 3.6 kg into grams.Show answer
Answer: 3,600 g
Q2Convert 2,450 ml into litres.Show answer
Answer: 2.45 litres
Q3A room is L-shaped: a large rectangle 7 m by 5 m, with a smaller rectangle 3 m by 2 m removed from one corner. What is the area of the room?Show answer
Answer: 29 square metres (35 - 6)
Q4A rectangular playground is 45 m long and 28 m wide. It is going to be fenced all the way round. How many metres of fencing are needed?Show answer
Answer: 146 m
Q5A parallelogram has a base of 15 cm and a perpendicular height of 6 cm. What is its area?Show answer
Answer: 90 square cm
Q6A triangular flag has a base of 30 cm and a perpendicular height of 18 cm. What is its area?Show answer
Answer: 270 square cm
Q7A fish tank in the shape of a cuboid is 60 cm long, 30 cm wide and 40 cm high. What is its volume?Show answer
Answer: 72,000 cubic cm
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A vegetable patch is L-shaped: a large rectangle 6 m by 5 m, with a smaller rectangle 2 m by 3 m removed from one corner. Topsoil costs 4 pounds per square metre to cover the patch. How much will it cost to cover the whole vegetable patch with topsoil?
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A box in the shape of a cuboid has a volume of 240 cubic cm. Its length is 8 cm and its width is 6 cm. What is its height?
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A market stall sells rolls of ribbon that are 250 cm long. A customer needs to cut lengths of ribbon that are each 0.4 m long, with no ribbon wasted. How many full lengths can be cut from one roll, and how much ribbon, in cm, is left over?
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Free printable worksheet
Want more practice on paper? Download the measurement: units, perimeter, area and volume worksheet pack - 6 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.
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