KS3 Maths · Year 7 · Chapter 6: Surface area and volume of prisms · Lesson 2

Surface area of prisms

Year 7About 70 minutesCalculator allowed51 marks

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Quick questions to start.

A1
Needed today
Work out the area of a triangle with base $8$ cm and height $5$ cm.
[1 mark]
Answer
A2
Needed today
A cube has edges of $3$ cm. Work out its total surface area.
[1 mark]
Answer
A3
Last lesson
Convert $5.2$ m² to cm².
[1 mark]
Answer
A4
From chapter 2
Three angles of a quadrilateral are $9 7^{\circ}$ , $6 4^{\circ}$ and $11 8^{\circ}$ . Work out the fourth angle.
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the total surface area of the triangular prism.

Not drawn accurately

Hint There are two equal right-angled triangles and three different rectangles. Each rectangle is one side of the triangle times the length of the prism.

B1
Work out the total surface area of the triangular prism.
[3 marks]
Not drawn accurately
Answer

Example 2

The prism has an L-shaped cross-section. Work out its total surface area.

Not drawn accurately

Hint Split the L into two rectangles to find its area. The rectangles round the sides together are the perimeter of the L times the length.

B2
The prism has an L-shaped cross-section. Work out its total surface area.
[4 marks]
Not drawn accurately
Answer

Example 3

The total surface area of the triangular prism is $312$ cm². Work out the length, $l$ , of the prism.

Not drawn accurately

Hint Write the surface area with

l

in it and set it equal to

312

B3
The total surface area of the triangular prism is $552$ cm². Work out the length, $l$ , of the prism.
[3 marks]
Not drawn accurately
Answer $l = \dots\dots$ cm

Practice

Year 7

C1
The cross-section of this prism is an isosceles triangle. Work out the total surface area of the prism.
[3 marks]
Not drawn accurately
Answer
C2
A box is a cuboid with no lid. It is $30$ cm long, $20$ cm wide and $12$ cm high. Work out the area of card used to make the box.
[3 marks]
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Answer

C3
A wooden chest is a cuboid. Work out its total surface area. Give your answer in m².
[3 marks]
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Answer
C4
The cross-section of this prism is a trapezium. Work out the total surface area of the prism.
[3 marks]
Not drawn accurately
Answer
C5
A cube has a total surface area of $294$ cm². Work out the length of one edge.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Mia works out the total surface area of this prism as $9 \times 10 + 12 \times 10 + 15 \times 10 = 360$ cm².
Mia's answer is wrong. Explain what she has done wrong, and work out the correct total surface area.
[3 marks]
Not drawn accurately
Answer $\dots\dots$ cm²

D2
Ola makes a concrete ramp. It is a prism with a right-angled triangle as its cross-section. The bottom of the ramp sits on the ground. She paints all the other faces.
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(a)
Work out the area she paints. Give your answer in m².
[4 marks]
Answer
(b)
One tin of paint covers $1.2$ m². How many tins does she need? Give a reason for your answer.
[2 marks]
Answer
Total for D2: 6 marks
D3
A chocolate box is a prism. Its cross-section is an equilateral triangle with sides of $4$ cm and an area of $6.9$ cm². The box is $20$ cm long. A factory makes $100$ boxes. Card is sold in sheets of $1$ m². How many sheets must the factory buy?
[4 marks]
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Answer
D4
A cuboid is $6$ cm long, $4$ cm wide and $h$ cm high. Its total surface area is $148$ cm². Work out the value of $h$ .
[3 marks]
Not drawn accurately
Answer $h = \dots\dots$
D5
Box $A$ is a cube with edges of $10$ cm. Box $B$ is a cuboid $20$ cm by $10$ cm by $5$ cm. Both boxes have the same volume. Which box needs less card to make? You must show your working.
[3 marks]
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Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
The cross-section of this prism is an isosceles triangle with base $b$ cm, equal sides of $17$ cm and height $15$ cm. The prism is $10$ cm long. Its total surface area is $740$ cm². Work out the value of $b$ .
[4 marks]
Not drawn accurately
Hint 1 · What to try
Write the area of the two triangles and the area of the three rectangles in terms of $b$ .
Hint 2 · The first line
The two triangles have area $2 \times \frac{1}{2} \times b \times 15 = 15 b$ . The rectangles have area $(b + 17 + 17) \times 10 = 10 b + 340$ .
Hint 3 · The full method
$15 b + 10 b + 340 = 740$ , so $25 b = 400$ and $b = 16$ .
Answer $b = \dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out the total surface area of a cuboid and of a triangular prism.
I can work out the surface area of a prism from its cross-section and its length.
I can work backwards from a surface area to find a length.

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