 5.01 Surface area of prisms and pyramids

Worksheet
Surface area of prisms
1

Find the surface area of the following cubes:

a
b
2

Find the surface area of a cube with a side length of 4\text{ cm}.

3

Find the side length of a cube with the following surface areas, correct two decimal places:

a
8166 \text{ cm}^{2}
b
600 \text{ cm}^{2}
4

A cube has surface area of 1032 \text{ cm}^{2}.

a

Find the area of one of the square faces.

b

Hence, find the length of one side of the cube, correct to two decimal places.

5

Find the surface area of the following rectangular prisms:

a
b
c
6

Find the surface area of the following triangular prisms:

a
b
c
7

Find the surface area of the following trapezoidal prisms:

a
b
8

Find the surface area of the following prism, correct to two decimal places:

9

For each of the following triangular prisms:

i

Find the value of x.

ii

Find the surface area.

a
b
10

Consider the following prism:

a

Find the height, h, correct to two decimal places.

b

Find the surface area, correct to one decimal place.

Surface area of pyramids
11

Find the surface area of the following pyramids:

a
b
c
d
12

Consider the following right pyramid:

a

Find the length of the slant height. Round your answer to two decimal places.

b

Hence, find the surface area of the right pyramid. Round your answer to one decimal place.

13

Consider the following square pyramid:

a

Find the length of the slant height. Round your answer to two decimal places.

b

Hence, find the surface area of the square pyramid. Round your answer to one decimal place.

14

Consider the rectangular pyramid with rectangular base of dimensions 6\text{ cm} by 8\text{ cm} and perpendicular height 6\text{ cm}:

a

Find the length of the slant height, x\text{ cm}, correct to two decimal places.

b

Find the length of the second slant height, y\text{ cm}, correct to two decimal places.

c

Find the surface area of the pyramid. Round your answer to one decimal place.

15

A small square pyramid of height 5\text{ cm} was removed from the top of a large square pyramid of height 10\text{ cm} to form the solid shown:

a

Find the length of the slant height of the sides of the new solid. Round your answer to two decimal places.

b

Find the surface area of the solid formed. Round your answer to one decimal place.

16

Find the surface area of a square pyramid with base edge 10\text{ cm} and perpendicular height 5\text{ cm}. Round your answer to two decimal places.

17

A square pyramid has a surface area of 480 \text{ cm}^2. The area of its square base is 36 \text{ cm}^2.

a

Find the area of each triangular face.

b

Find the slant height of each triangular face, correct to two decimal places.

c

Find the perpendicular height of the pyramid, correct to one decimal place.

Applications
18

Laura is building a storage chest in the shape of a rectangular prism. The chest will be 55\text{ cm} long, 41\text{ cm} deep, and 39\text{ cm} high. Find the surface area of the chest.

19

A birthday gift is placed inside the box shown, which has the shape of a rectangular prism.

Find the minimum amount of wrapping paper needed to cover this box.

20

A swimming pool has the shape of a trapezoidal prism 14\text{ m} long and 6 \text{ m} wide. The depth of the water ranges from 1.2\text{ m} to 2.5 \text{ m}, as shown in the diagram.

The walls and base of the pool are going to be tiled. Calculate the total area inside the pool that is to be tiled. Round your answer to one decimal place.

21

Some very famous right square pyramids are the Egyptian Pyramids. The Great Pyramid which has a base of 230 \text{ m} and a slant height of 216 \text{ m}.

Find the surface area of the Great Pyramid.

22

The roof of a large public building is in the shape of a rectangular pyramid, as shown below:

a

Calculate the surface area of the roof, excluding the base of the pyramid. Round your answer to the nearest square metre.

b

Each tile used on the roof has an area of 600\text{ cm}^2. How many tiles are used to cover the roof?

23

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 perpendicular height of 22\text{ m} and a base length of 35 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? Round your answer to the nearest square metre.

24

The high rise building shown has vertical sides made entirely from glass panels:

How many square metres of glass make up the building's walls?

25

Consider the high rise building shown below:

a

Find the surface area of the walls of the building.

b

If 2\% of the area of the walls is taken up by metal frames and the rest is glass, how many square metres of glass are used on the walls?