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Lesson 12 of 16
New
New
- Year 8
Surface area of prisms
I can find the surface area of 3D shapes in an efficient way.
Lesson details
Key learning points
- The surface area of a 3D shape is the sum of the area of all the faces.
- The net of a prism can help find the surface area of a prism but can be time consuming.
- By using known area facts, the area of all the faces can be found and summed.
- It is important to find the surface area systematically and efficiently.
Keywords
Prism - polyhedron with base and identical parallel opposite side with corresponding edges joined by parallelograms.
Faces - Faces are the flat 2D surfaces of a 3D shape.
Nets - The net of a 3D object is a 2D representation of its faces that can be folded up into the 3D object.
Surface area - The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Common misconception
Pupils may try to avoid sketching of nets or faces and in turn miss information.
Reassure pupils that a sketch does not need to be perfect and just needs to convey the key information.
If you have access to physical models of prisms and nets, they can support pupils who may struggle with visualising the unfolding. Having nets to demonstrate the folding and unfolding is helpful.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.The area of a rectangle with a width of 7 cm and a length of 12 m is m².
The area of a rectangle with a width of 7 cm and a length of 12 m is m².
Correct Answer: 84, eighty four
84, eighty four
Q2.The area of a triangle with a base length of 14 cm and a perpendicular height of 8 cm is cm².
The area of a triangle with a base length of 14 cm and a perpendicular height of 8 cm is cm².
Correct Answer: 56, fifty six, 56 cm², 56cm²
56, fifty six, 56 cm², 56cm²
Q3.The area of a trapezium is being calculated $${\text {Area}}={{1}\over{2}} \times {(6+16)} \times {12} = 132 \text{ cm}^2$$. What is the perpendicular height of this trapezium?
The area of a trapezium is being calculated $${\text {Area}}={{1}\over{2}} \times {(6+16)} \times {12} = 132 \text{ cm}^2$$. What is the perpendicular height of this trapezium?
6
Correct answer: 12
12
16
22
Q4.A prism is a polyhedron with a base that is a and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.
A prism is a polyhedron with a base that is a and a parallel opposite face that is identical. The corresponding edges of the two polygons are joined by parallelograms.
Correct Answer: polygon
polygon
Q5.The perimeter of this shape is cm.
The perimeter of this shape is cm.
Correct Answer: 46, 46 centimetres, forty six centimetres, 46 cm, 46cm
46, 46 centimetres, forty six centimetres, 46 cm, 46cm
Q6.Match the shape of the base with the name of the prism.
Match the shape of the base with the name of the prism.
Correct Answer:rectangular base ,cuboid
rectangular base - cuboid
Correct Answer:square base,cube
square base - cube
Correct Answer:pentagonal base,pentagonal prism
pentagonal base - pentagonal prism
Correct Answer:triangular base,triangular prism
triangular base - triangular prism
Assessment exit quiz
6 Questions
Q1.The surface area is the area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
The surface area is the area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Correct Answer: total
total
Q2.Which of these are nets for a cube?
Which of these are nets for a cube?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q3.Here is a right prism. Which of these descriptions is correct?
Here is a right prism. Which of these descriptions is correct?
The prism has 6 different shaped faces.
The prism has 6 faces, two are parallelograms and four are rectangles.
Correct answer: The prism has 6 faces, two are trapeziums and four are rectangles.
The prism has 6 faces, two are trapeziums and four are rectangles.
The prism has 6 faces, two are isosceles triangles and four are rectangles.
Q4.The areas of the faces of a triangular prism are $$24\text{ cm}^2,24\text{ cm}^2,50\text{ cm}^2, 40\text{ cm}^2\text{ and }30\text{ cm}^2$$ respectively. The surface area is $$\text{ cm}^2$$.
The areas of the faces of a triangular prism are $$24\text{ cm}^2,24\text{ cm}^2,50\text{ cm}^2, 40\text{ cm}^2\text{ and }30\text{ cm}^2$$ respectively. The surface area is $$\text{ cm}^2$$.
Correct Answer: 168
168
Q5.The surface area of this right-angled isosceles triangular prism is $$\text{ cm}^2$$.
The surface area of this right-angled isosceles triangular prism is $$\text{ cm}^2$$.
Correct Answer: 240.2
240.2
Q6.In a right prism, the rectangular faces can be seen as one large rectangle. The dimensions of the large rectangle are the of the base by the length of the prism.
In a right prism, the rectangular faces can be seen as one large rectangle. The dimensions of the large rectangle are the of the base by the length of the prism.
Correct Answer: perimeter
perimeter
