Name of Lecturer: Mr. J.Agius
Course: HVAC2
Lesson 24
Chapter 2. Perimeter, Area & Volume
Cubes and Cuboids
Cuboids, Rectangular Prisms and Cubes
A cuboid is a box-shaped object. It has six
flat sides and all angles are right angles.
And all of its faces are rectangles.
It is also a prism because it has the same
cross-section along a length. In fact it is a
rectangular prism.
If at least two of the lengths are equal then it can
also be called a square prism.
(Note that this doesn't stop it from also being called a
rectangular prism if you want!)
If all three lengths are equal it can be called a
cube and each face will be a square.
A cube is still a prism.
So a cube is just a special case of a square prism, and
a square prism is just a special case of a rectangular prism.
And they are all cuboids.
2. Perimeter, Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC2
Note: The name "cuboid" comes from "cube" and -oid (which
means "similar to, or resembling") and so indicates "it is like a
cube".
Another use of -oid is when we talk about the Earth being a
spheroid (not exactly a sphere, but close).

Surface Area
The surface area is:
A = 2wd + 2dh + 2hw
Example Calculation
Find the Surface area of this cuboid.
A = 2×4×5 + 2×5×10 + 2×10×4
= 40+100+80 = 220

Examples of Cuboids
Cuboids are very common in our world, from boxes to buildings we see them everywhere.
You can even fit them inside other cuboids!
A box with a slot
cut as a handle
Cuboids in a cuboid
room
2. Perimeter, Area & Volume
Boxes for model trains
Now that's just silly!
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Name of Lecturer: Mr. J.Agius
Course: HVAC2
The Surface Area of a Cuboid
A cuboid has six faces of which opposite pairs are identical. The total surface area of a cuboid is
therefore given by adding the areas of three different faces and doubling the result.
5 cm
11 cm
For the cuboid shown,
The area of the top (or base) is
The area of the front face is
The area of an end is
3 cm
11 × 3 cm2 = 33 cm2
11 × 5 cm2 = 55 cm2
3 × 5 cm2 = 15 cm2
Therefore the total surface area is 2 × (33 + 55 + 15) cm2 = 206 cm2
This can be seen very clearly if we draw a net of the cuboid, i.e. the flat shape obtained when the
cuboid is cut along some of its edges and flattened out.
For example if the cuboid above is cut along the thick edges and opened up, this net is produced.
11 × 3 cm2
11 × 5 cm2
5 × 3 cm2
11 × 3 cm2
5 × 3 cm2
11 × 5 cm2
2. Perimeter, Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC2
Exercise 1
1)
Calculate the Surface area of a cube of side:
a)
8cm
2)
In this question find the surface area of the cuboid given by the net.
b)
11cm
a)
c)
4.1cm
35cm
b)
1.5cm
70cm
2cm
3cm
3)
30cm
A scout’s tent has the shape of a triangular prism. It is 2.6 m long and the triangular end
is 2.5 m wide and 1.9 m high.
a)
Draw the net of this tent.
b)
What is the area of canvas, including the ground sheet, used to make this tent?
4)
The parallel sides of a trapezium are 3.2 cm apart and their lengths are 7.6 cm and 5.3
cm, all measurements being correct to 2 s.f. Find, the area of the trapezium.
5)
The diagram represents a chocolate box in the shape of a pyramid. The box has a square
base and four triangular faces. The net of the chocolate box is shown.
a)
Work out
(i)
the area of the base
(ii)
the area of the triangular face
(iii)
the total surface area of the box
3cm
3cm
4cm
4cm
2. Perimeter, Area & Volume
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Name of Lecturer: Mr. J.Agius
6)
Course: HVAC2
In the following diagrams:
a)
sketch a net for the given prism.
b)
find the total surface area of the prism.
c)
find the volume of the prism.
10 cm
i)
ii)
5 cm
4 cm
5 cm
4 cm
8 cm
5 cm
10 cm
4 cm
7 cm
iii)
iv)
4 cm
5 cm
4 cm
3 cm
9 cm
7)
6 cm
In the diagram the side of each grid square represents 1 cm. Find the shaded area. (Look
for the quickest method, in which only two separate areas need be calculated.)
2. Perimeter, Area & Volume
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Name of Lecturer: Mr. J.Agius
Course: HVAC2
8)
On this square paper, using the side of one square to represent 1 cm, draw a triangle with
vertices at (4, -3), (-1, 4) and (3, 6). Find its area by enclosing it in a rectangle.
9)
Find
a)
the height of triangle ABC
b)
the area of the trapezium shown in the diagram.
2 cm
6 cm2
3 cm
2. Perimeter, Area & Volume
10 cm
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