Topics
12. Geometry
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AustraliaNSW
Stage 3

12.05 Prisms, pyramids, and other 3D solids

Lesson
Practice
Lesson

Are you ready?

Being able to identify the  key features of shapes  can help us in this lesson.

Examples

Example 1

How many edges does each shape have?

a
The image shows a square.
Worked Solution
Create a strategy

We can count the straight lines around the square.

Apply the idea

The square has 4 straight lines around it.

So it has 4 edges.

b
The image shows a kite.
Worked Solution
Create a strategy

We can count the straight lines around the kite.

Apply the idea

The kite has 4 straight lines around it.

So it has 4 edges.

Idea summary

An edge is a straight line that makes part of the perimeter of a shape.

Prisms

This video looks at prisms, it starts with showing how a prism is made by looking at its net, and then looks at the faces, edges and vertices of a prism.

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Examples

Example 2

Here is a rectangular prism.

An image of a rectangular prism.
a

How many faces does it have?

Worked Solution
Create a strategy

Faces are the flat sides of a solid.

Apply the idea

It has 6 faces.

b

How many vertices does it have?

Worked Solution
Create a strategy

Vertices are the corners where edges meet.

Apply the idea

It has 8 vertices.

c

How many edges does it have?

Worked Solution
Create a strategy

An edge is the line where two faces meet.

Apply the idea

It has 12 edges.

Idea summary

A prism can be made with any polygon at its base.

Pyramids

This video looks at pyramids, it starts with showing how a pyramid is made by looking at its net, and then looks at the faces, edges and vertices of a pyramid.

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Examples

Example 3

Here is a square pyramid:

A square pyramid.
a

How many faces does it have?

Worked Solution
Create a strategy

Faces are the flat sides of a solid object.

Apply the idea

It has 5 faces: the 4 triangles and the 1 square base.

b

How many vertices does it have?

Worked Solution
Create a strategy

Vertices are the corners where two edges meet.

Apply the idea

It has 5 vertices.

c

How many edges does it have?

Worked Solution
Create a strategy

An edge is where two faces meet.

Apply the idea

It has 8 edges.

Idea summary

Pyramids can have different bases, and the name of the base tells us the name of the pyramid.

Cones, spheres, and cylinders

This video looks at cones, spheres, and cylinders. All these shapes have curved surfaces. Let's see how we can tell which one is which.

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Examples

Example 4

Here is a cone.

A cone.
a

How many curved surfaces does it have?

Worked Solution
Create a strategy

A curved surface is a surface that is not flat.

Apply the idea

There is 1 curved surface that wraps around the circle at base and goes up to the vertex at the top.

b

How many vertices does it have?

Worked Solution
Create a strategy

In a cone, the vertex is the top point.

Apply the idea

It has 1 vertex.

c

How many edges does it have?

Worked Solution
Create a strategy

An edge is a straight line segment where two faces meet.

Apply the idea

It has 1 curved edge around the circle.

Idea summary

Cones, spheres and cylinders all have curved faces.

Outcomes

MA3-14MG

identifies three-dimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views

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