1. We are Learning to……
Find Surface Area

2. Surface area of a rectangular prism
To find the surface area of a shape, we calculate the total area of all of the faces.
A rectangular prism has 6 faces.
The top and the bottom of the rectangular prism have the same area.
Discuss the meaning of surface area. The important thing to remember is that although surface area is found for three-dimensional shapes, surface area only has two dimensions. It is therefore measured in square units.

3. Surface area of a rectangular prism
To find the surface area of a shape, we calculate the total area of all of the faces.
A rectangular prism has 6 faces.
The front and the back of the rectangular prism have the same area.

4. Surface area of a rectangular prism
To find the surface area of a shape, we calculate the total area of all of the faces.
A rectangular prism has 6 faces.
The left hand side and the right hand side of the rectangular prism have the same area.

5. Surface area of a rectangular prism
To find the surface area of a shape, we calculate the total area of all of the faces.
Can you work out the surface area of this rectangular prism?
5 cm
8 cm
The area of the top = 8 × 5
= 40 cm2
7 cm
The area of the front = 7 × 5
= 35 cm2
The area of the side = 7 × 8
= 56 cm2

6. Surface area of a rectangular prism
To find the surface area of a shape, we calculate the total area of all of the faces.
So the total surface area =
5 cm
8 cm
2 × 40 cm2
Top and bottom
7 cm
+ 2 × 35 cm2
Front and back
Stress the importance to work systematically when finding the surface area to ensure that no faces have been left out.
We can also work out the surface area of a cuboid by drawing its net (see slide 51). This may be easier for some pupils because they would be able to see every face rather than visualizing it.
+ 2 × 56 cm2
Left and right side
= = 262 cm2

7. Formula for the surface area of a rectangular prism
We can find the formula for the surface area of a rectangular prism as follows.
Surface area of a rectangular prism = h l w
2 × lw
Top and bottom
+ 2 × hw
Front and back
Pupils should write this formula down.
+ 2 × lh
Left and right side
= 2lw + 2hw + 2lh

8. How can we find the surface area of a cube of length x?
All six faces of a cube have the same area. x
The area of each face is x × x = x2
Therefore,
As pupils to use this formula to find the surface area of a cube of side length 5 cm.
6 × 52 = 6 × 25 = 150 cm2.
Repeat for other numbers.
As a more challenging question tell pupils that a cube has a surface area of 96 cm2. Ask them how we could work out its side length using inverse operations.
Surface area of a cube = 6x2

9. Chequered rectangular prism problem
This cuboid is made from alternate purple and green centimetre cubes.
What is its surface area?
Surface area
= 2 × 3 × × 3 × × 4 × 5 =
= 94 cm2
Discuss how to work out the surface area that is green.
Ask pupils how we could write the proportion of the surface area that is green as a fraction, as a decimal and as a percentage.
How much of the surface area is green?
48 cm2

10. What is the surface area of this L-shaped prism?
Surface area of a prism
What is the surface area of this L-shaped prism?
3 cm
To find the surface area of this shape we need to add together the area of the two L-shapes and the area of the 6 rectangles that make up the surface of the shape.
3 cm
4 cm
6 cm
Discuss ways to find the surface area of this solid. We could use a net of this prism to help find the area of each face.
Total surface area
= 2 ×
5 cm
= 110 cm2

11. Using nets to find surface area
It can be helpful to use the net of a 3-D shape to calculate its surface area.
Here is the net of a 3 cm by 5 cm by 6 cm rectangular prism.
5 cm
6 cm
3 cm
Write down the area of each face.
18 cm2
Then add the areas together to find the surface area.
15 cm2
Links:
S3 3-D shapes – nets
S6 Construction and Loci – constructing nets
30 cm2
15 cm2
30 cm2
18 cm2
Surface Area = 126 cm2

12. Using nets to find surface area
Here is the net of a regular tetrahedron.
What is its surface area?
Area of each face = ½bh
= ½ × 6 × 5.2
= 15.6 cm2
5.2 cm
Surface area = 4 × 15.6
= 62.4 cm2
6 cm

13. McGraw-Hill Page 32 #s 1 – 9 BLM 1-11 #s 3,5,8,11,13
To succeed at this lesson today you need to…
1. Find the total area of the faces
2. Use a net where appropriate
3. Don’t forget the units
McGraw-Hill Page 32 #s 1 – 9 BLM 1-11 #s 3,5,8,11,13

14. Homework
McGraw – Hill Page 34 #s 11 – 13 & 16