Measurement: Units, Perimeter, Area and Volume - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 5)Measurement: Units, Perimeter, Area and Volume revision guide

This topic is chapter 9 of KS2 Maths: Measurement Practice Book.

7.10 Measurement: Units, Perimeter, Area and Volume

Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Convert the measurements.

(a)Write 4.2 kilometres in metres.(1)

(b)Write 3,450 millimetres in metres.(1)

A rectangular plot measures 1500 cm by 90 m. Convert the shorter side to metres then find the perimeter of the plot in metres.

(2)

Explain whether this statement is always, sometimes or never true. "If two triangles have the same base and the same area, then they must have the same height." Explain your answer.

(2)

A triangular flower bed has base 6 m and height 2.4 m. It is surrounded by a 0.6 m wide border. What is the area of the border to one decimal place in square metres? (Assume the border follows similar triangular shape.)

(3)

A metal sheet is a parallelogram with side lengths 12 cm and 7 cm. The perpendicular distance (height) between the 12 cm sides is 5 cm. Calculate the area of the sheet in square centimetres.

(2)

A box's external dimensions are 32 cm by 20 cm by 15 cm. The box wall is uniform and 1 cm thick. Estimate the internal volume of the box in cubic centimetres.

(2)

A rectangle has area 54 cm2. One side measures 6 cm. Find the length of the other side.

(2)

A water tank is a cuboid with length 2.4 m, width 1.5 m and height 1.2 m. A pump removes 540 litres. How much water remains in the tank in litres? (1 m3 = 1000 litres)

(3)

A playground has a triangular sand area with vertices A, B and C. BC = 12 m is the base of the triangle and the perpendicular height from BC to vertex A is 6 m. AB = 9 m. Work out the area of the sand in square metres.

(2)

A rectangle and a parallelogram have the same base 10 cm and the same area 80 cm2. Explain how you could find the height of the parallelogram and give the height.

(3)

A garden path is 7.5 m long and 80 cm wide. Work out its area in square metres.

(2)

A school field is a rectangle 120 m by 85 m. A path 2 m wide goes all around the edge inside the field. What is the area of the path in square metres?

(2)

Find the perimeter of an L-shaped garden made from two rectangles. The larger rectangle is 8 m by 5 m. A smaller rectangle (cut from one corner) is 3 m by 2 m as shown: what is the perimeter of the L-shape in metres?

Figure: Imagine a rectangle 8 by 5 with a 3 by 2 rectangle removed from one corner; pupils should work from dimensions.

(2)

The area of a triangle is 48 cm2. The base is 12 cm. Work out the height of the triangle.

(3)

A parallelogram has base 14 cm and height 6 cm. Calculate its area in square centimetres.

(2)

A cuboid has length 8 cm, width 5 cm and height 3 cm. Calculate its volume in cubic centimetres.

(2)

A fish tank is a cuboid with internal dimensions 90 cm by 40 cm by 50 cm. A gardener fills the tank to a depth of 30 cm with water. What volume of water is in the tank in litres? (1 litre = 1000 cm3)

(3)

A rectangular carpet is 3.2 m long and 2.5 m wide. Work out its area in square metres, giving your answer to one decimal place.

(2)

Mark scheme · 7.10 Measurement: Units, Perimeter, Area and Volume

Question 1

(a) B1 4,200 cao
(a) Answer: 4,200
(b) B1 3.45 cao
(b) Answer: 3.45

Question 2

M1 convert 1500 cm to 15 m then set up perimeter 2(15+90)
B1 210 cao
Answer: 210

Question 3

M1 state that area = 1/2 x base x height and use reasoning
B1 conclude statement is sometimes true with explanation that different heights could be compensated by different bases (or vice versa) or show counterexample reasoning
Answer: sometimes

Question 4

M1 find outer similar triangle dimensions: base 6+2*0.6 = 7.2 and height 2.4+2*0.6 = 3.6
M1 calculate outer area 1/2 x 7.2 x 3.6 and inner area 1/2 x 6 x 2.4 and subtract
B1 5.8 cao
Answer: 5.8

Question 5

M1 use area = base x height with base 12 and height 5
B1 60 cao
Answer: 60

Question 6

M1 subtract twice the thickness from each external dimension: internal dims 30 x 18 x 13
B1 7020 cao
Answer: 7020

Question 7

M1 divide area by one side: 54 / 6
B1 9 cm cao
Answer: 9 cm

Question 8

M1 calculate volume in m3: 2.4 x 1.5 x 1.2
M1 convert to litres by x1000 then subtract 540
B1 3,780 cao
Answer: 3780

Question 9

M1 use area = 1/2 x base x height with base 12 and height 6
B1 36 cao
Answer: 36

Question 10

M1 state formula area = base x height for parallelogram or area = base x height for rectangle
M1 rearrange to height = area / base and substitute values
B1 8 cm cao
Answer: 8 cm

Question 11

M1 convert 80 cm to 0.8 m or equivalent and set up 7.5 x 0.8
B1 6.0 cao
Answer: 6.0

Question 12

M1 subtract inner rectangle area from outer: (120 x 85) - (116 x 81) or equivalent
B1 804 cao
Answer: 804

Question 13

M1 identify the outer outline sides: lengths 8, 5, (8-3)=5, (5-2)=3, 3, 2 or equivalent
B1 26 cao
Answer: 26

Question 14

M1 use area = 1/2 x base x height or rearrange to height = (2 x area) / base
M1 substitute values: height = (2 x 48) / 12
B1 8 cm cao
Answer: 8 cm

Question 15

M1 use area = base x height
B1 84 cao
Answer: 84

Question 16

M1 use volume = length x width x height
B1 120 cao
Answer: 120

Question 17

M1 calculate volume in cm3: 90 x 40 x 30 or equivalent
M1 convert cm3 to litres by dividing by 1000
B1 108 litres cao
Answer: 108

Question 18

M1 calculate 3.2 x 2.5
B1 8.0 cao
Answer: 8.0

Measurement: Units, Perimeter, Area and Volume - Worksheets, Questions and Revision

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