Perimeter, Area and Volume (11+ Maths) - Worksheets, Questions and Revision

20 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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11+ · Mathematics

EP.M11 Perimeter, Area and Volume

GL ASSESSMENT GL · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A rectangle has length 9 cm and width 4 cm. Calculate the perimeter of the rectangle.

(Total for Question 1 is 2 marks)

A rectangle has length 8 cm and width 5 cm. Calculate the area of the rectangle.

(Total for Question 2 is 2 marks)

A regular hexagon has sides of length 5 cm. Calculate the perimeter of the hexagon.

Diagram NOT accurately drawn

(Total for Question 3 is 2 marks)

A cube has edges of length 4 cm. Calculate the volume of the cube.

(Total for Question 4 is 2 marks)

A square has a perimeter of 36 cm. Calculate the area of the square.

(Total for Question 5 is 2 marks)

A triangle has a base of 12 cm and a perpendicular height of 7 cm. Calculate the area of the triangle.

(Total for Question 6 is 2 marks)

A parallelogram has a base of 10 cm and a perpendicular height of 6 cm. Calculate the area of the parallelogram.

(Total for Question 7 is 2 marks)

A trapezium has parallel sides of length 8 cm and 12 cm, and a perpendicular height of 5 cm. Calculate the area of the trapezium.

(Total for Question 8 is 3 marks)

A garden ornament is made from a rectangle with a triangle on top, forming a simple house-shaped outline. The rectangle is 10 cm wide and 6 cm tall. The triangle on top has a base of 10 cm and a perpendicular height of 4 cm. Calculate the total area of the shape.

Diagram NOT accurately drawn

(Total for Question 9 is 3 marks)

The diagram shows an L-shaped garden path formed from a 12 cm by 10 cm rectangle with a 5 cm by 4 cm rectangle removed from the top right corner (dimensions shown are the outer rectangle sides and the notch removed; not drawn to scale).

Diagram NOT accurately drawn

(a)Calculate the perimeter of the L-shape.(3)

(b)Calculate the area of the L-shape.(3)

(Total for Question 10 is 6 marks)

A cuboid has length 7 cm, width 4 cm and height 3 cm. Calculate the volume of the cuboid.

(Total for Question 11 is 3 marks)

A cuboid has length 5 cm, width 3 cm and height 4 cm. Calculate the total surface area of the cuboid.

(Total for Question 12 is 3 marks)

A circle has a radius of 10 cm. Take π = 3.14.

Diagram NOT accurately drawn

(a)Calculate the circumference of the circle.(2)

(b)Calculate the area of the circle.(2)

(Total for Question 13 is 4 marks)

A rectangular picture frame has a length of 2.5 m and a width of 80 cm. Calculate the perimeter of the frame in metres.

(Total for Question 14 is 3 marks)

A rectangular garden measures 15 m by 9 m. Fencing costs 4.50 pounds sterling per metre.

(a)Calculate the perimeter of the garden.(2)

(b)Calculate the total cost of fencing the whole perimeter of the garden.(2)

(Total for Question 15 is 4 marks)

A rectangular room measures 6 m by 4 m. Carpet costs 12 pounds sterling per square metre.

(a)Calculate the area of the room.(2)

(b)Calculate the total cost of carpeting the whole room.(2)

(Total for Question 16 is 4 marks)

A solid cuboid measures 10 cm by 8 cm by 6 cm. A smaller cuboid measuring 4 cm by 3 cm by 6 cm is cut out of one vertical edge, running the full height of the solid. Calculate the volume of the remaining solid.

Diagram NOT accurately drawn

(Total for Question 17 is 4 marks)

A semicircular table top has a diameter of 14 cm. Take π = 22/7. Calculate the perimeter of the semicircle (the curved edge plus the straight edge).

Diagram NOT accurately drawn

(Total for Question 18 is 3 marks)

A rectangular lawn measures 10 m by 6 m. A path of uniform width 1 m is built all the way around the outside of the lawn. Calculate the area of the path only.

Diagram NOT accurately drawn

(Total for Question 19 is 4 marks)

A cuboid water tank has length 40 cm, width 25 cm and height 20 cm.

(a)Calculate the volume of the tank in cm³.(2)

(b)Water is poured into the tank until it is 3/4 full. Calculate the volume of water in the tank.(2)

(c)Given that 1000 cm³ = 1 litre, calculate how many litres of water this is.(2)

(Total for Question 20 is 6 marks)

Mark scheme · EP.M11 Perimeter, Area and Volume

Question 1

M1 correct method, e.g. 9 + 4 + 9 + 4 or 2 x (9 + 4)
A1 26 cm cao
Answer: 26 cm

Question 2

M1 8 x 5 seen
A1 40 cm² cao
Answer: 40 cm²

Question 3

M1 6 x 5 seen (or 5 added six times)
A1 30 cm cao
Answer: 30 cm

Question 4

M1 4 x 4 x 4 seen (or 4³)
A1 64 cm³ cao
Answer: 64 cm³

Question 5

M1 side length found: 36 / 4 = 9 cm
A1 81 cm² cao
Answer: 81 cm²

Question 6

M1 0.5 x 12 x 7 seen
A1 42 cm² cao
Answer: 42 cm²

Question 7

M1 10 x 6 seen
A1 60 cm² cao
Answer: 60 cm²

Question 8

M1 8 + 12 = 20 seen
M1 0.5 x 20 x 5 seen (oe)
A1 50 cm² cao
Answer: 50 cm²

Question 9

M1 rectangle area 10 x 6 = 60 cm²
M1 triangle area 0.5 x 10 x 4 = 20 cm²
A1 80 cm² cao (ft their two areas added)
Answer: 80 cm²

Question 10

(a) M1 missing lengths found: 12 - 5 = 7 cm and 10 - 4 = 6 cm
(a) M1 all six sides added: 12 + 6 + 5 + 4 + 7 + 10
(a) A1 44 cm cao
(a) Answer: 44 cm
(b) M1 large rectangle area 12 x 10 = 120 cm²
(b) M1 removed rectangle area 5 x 4 = 20 cm²
(b) A1 100 cm² cao (ft 120 - their removed area)
(b) Answer: 100 cm²

Question 11

M1 correct substitution into V = l x w x h
M1 7 x 4 = 28 (or equivalent correct intermediate step)
A1 84 cm³ cao
Answer: 84 cm³

Question 12

M1 three face areas found: 5x3 = 15, 5x4 = 20, 3x4 = 12
M1 15 + 20 + 12 = 47 doubled
A1 94 cm² cao
Answer: 94 cm²

Question 13

(a) M1 2 x 3.14 x 10 seen (or 3.14 x 20)
(a) A1 62.8 cm cao
(a) Answer: 62.8 cm
(b) M1 3.14 x 10 x 10 seen
(b) A1 314 cm² cao
(b) Answer: 314 cm²

Question 14

M1 80 cm converted to 0.8 m
M1 2 x (2.5 + 0.8) seen (oe)
A1 6.6 m cao
Answer: 6.6 m

Question 15

(a) M1 2 x (15 + 9) seen
(a) A1 48 m cao
(a) Answer: 48 m
(b) M1 their (a) x 4.50 (ft)
(b) A1 216 pounds cao
(b) Answer: 216 pounds sterling

Question 16

(a) M1 6 x 4 seen
(a) A1 24 m² cao
(a) Answer: 24 m²
(b) M1 their (a) x 12 (ft)
(b) A1 288 pounds cao
(b) Answer: 288 pounds sterling

Question 17

M1 large cuboid volume 10 x 8 x 6 = 480 cm³
M1 removed cuboid volume 4 x 3 x 6 = 72 cm³
M1 480 - 72 seen (ft)
A1 408 cm³ cao
Answer: 408 cm³

Question 18

M1 full circumference found: 22/7 x 14 = 44 cm
M1 half of 44 (= 22) added to the diameter 14 (oe)
A1 36 cm cao
Answer: 36 cm

Question 19

M1 outer dimensions found: 12 m by 8 m
M1 outer area 12 x 8 = 96 m²
M1 lawn area 10 x 6 = 60 m²
A1 36 m² cao (ft 96 - their lawn area)
Answer: 36 m²

Question 20

(a) M1 40 x 25 x 20 seen
(a) A1 20000 cm³ cao
(a) Answer: 20000 cm³
(b) M1 their (a) x 3/4 (ft)
(b) A1 15000 cm³ cao
(b) Answer: 15000 cm³
(c) M1 their (b) / 1000 (ft)
(c) A1 15 litres cao
(c) Answer: 15 litres

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