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1.045 Surface area of pyramids

Worksheet
Surface area of pyramids
1

Consider this regular square pyramid.

a

How many identical triangular faces does it have?

b

Find the area of one triangular face.

c

Find the total surface area of the triangular faces of the pyramid.

d

Hence, find the total surface area of the pyramid.

2

Find the surface area of the following pyramids.

a
b
c
d
3

Consider this regular pentagonal pyramid and its net.

a

How many identical triangular faces does it have?

b

Find the area of one triangular face.

c

Find the total surface area of the triangular faces of the pyramid.

4

Find the total surface area of the triangular faces of the regular hexagonal pyramid shown:

Applications
5

Some very famous right square pyramids are the Egyptian pyramids located at the Giza Pyramid Complex.

The largest of the pyramids at the site is the Great Pyramid, which has a base of 230 \text{ m} and each of its triangular faces have a height of 216 \text{ m}.

Find the surface area of the Great Pyramid, not including the base.

6

The Louvre pyramid is a large glass and metal pyramid which serves as the entrance to the Louvre museum in Paris. It is a square pyramid with a base length of 35 \text{ m} and each of its triangular faces have a height of 28 \text{ m}.

If the surface of the pyramid (excluding the base) is entirely covered in glass, how many square metres of glass make up the structure?

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Outcomes

ACMEM096

find the surface area of pyramids, such as rectangular- and triangular-based pyramids

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