New
New
Year 8

Properties of prisms

I can appreciate that all prisms have two congruent polygonal parallel faces (bases) with parallelogram faces joining the corresponding vertices of the bases.

New
New
Year 8

Properties of prisms

I can appreciate that all prisms have two congruent polygonal parallel faces (bases) with parallelogram faces joining the corresponding vertices of the bases.

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Lesson details

Key learning points

  1. Prisms are 3D shapes with a cross-section that is a uniform polygon.
  2. All prisms will have a pair of parallel faces that are congruent.
  3. This polygon cross section is often used to name the prism.
  4. The sides connecting the bases are parallelograms.

Keywords

  • Prism - A prism is a polyhedron with a base that is a polygon and a parallel opposite face that is identical.

  • Cross-section - A cross section is a 2D face made from cutting straight through any plane of a 3D object.

Common misconception

I can tell a 3D shape is a prism because the 2D faces on both ends are congruent.

The cross-sectional face must be the same throughout, not just at the two ends of the shape. Also, the two end faces must be parallel.

The non-cross-sectional faces of a prism can be any type of parallelogram, thus all prisms are oblique. If these parallelograms are rectangles, then the prism is a special case of an oblique prism: the right prism.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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6 Questions

Q1.
Which of these polygons has exactly six sides?
quadrilateral
pentagon
Correct answer: hexagon
octagon
polygon
Q2.
Match each polygon to the number of sides it has.
Correct Answer:equilateral triangle,3

3

Correct Answer:parallelogram,4

4

Correct Answer:pentagon,5

5

Correct Answer:octagon,8

8

Correct Answer:pentadecagon,15

15

Q3.
This is a triangular-based pyramid. This 3D shape has 4 vertices and 6 edges. It has faces.
An image in a quiz
Correct Answer: 4, 4 faces, 4faces
Q4.
This is a triangular prism. Match the property of this object to its value.
An image in a quiz
Correct Answer:vertices,6

6

Correct Answer:edges,9

9

Correct Answer:faces,5

5

Q5.
The front face of this cuboid is parallel to which other face?
An image in a quiz
top face
bottom face
left face
right face
Correct answer: back face
Q6.
The front and right faces of this cuboid have equal area. Which faces of this cuboid are congruent to the front face?
An image in a quiz
top face
bottom face
Correct answer: left face
Correct answer: right face
Correct answer: back face

6 Questions

Q1.
Which of these 3D shapes are prisms?
An image in a quiz
Correct answer: a
b
Correct answer: c
d
Q2.
This 3D shape is a prism. The base face and cross-section shown were used to help identify this shape as a prism. Which of these statements must be true?
An image in a quiz
Correct answer: The base face and cross-section must be parallel to each other.
The base face and cross-section must be perpendicular to each other.
Correct answer: The base face and cross-section must be congruent to each other.
The base face and cross-section must be equidistant to each other.
The base face and cross-section must both be parallelograms.
Q3.
Which of these names are appropriate for this prism?
An image in a quiz
isosceles hexagonal prism
Correct answer: hexagonal prism
regular hexagonal prism
Correct answer: irregular hexagonal prism
Correct answer: right hexagonal prism
Q4.
Which of these words can used as part of the name of this prism?
An image in a quiz
right
Correct answer: oblique
parallelogram
Correct answer: trapezium
Correct answer: isosceles
Q5.
Alex says: "This prism is a rectangular prism, because this face is a rectangle". Which of these statements is correct?
An image in a quiz
Alex is correct because parallel cross-sections to this face are all rectangles.
Correct answer: Alex is incorrect because this is not the face that is the cross-sectional base.
Correct answer: This prism is a right angled triangular prism.
This prism is definitely a right prism because there is a right angle.
Q6.
Match each property of an octagonal prism to its value.
Correct Answer:number of vertices,16

16

Correct Answer:number of edges,24

24

Correct Answer:number of parallelogram faces,8

8

Correct Answer:number of octagonal faces,2

2

Correct Answer:number of total faces,10

10