1. Mathematics
Surface Area

2. Lesson Objectives The aim of this powerpoint is to help you…
to review the nets of common 3D shapes
to apply the methods for finding the area of rectilinear shapes to finding the surface area of common 3D shapes

3. Cubes
You should be able to recognise the net of a cube… remember a cube has 6 square faces
The area of one face = length × width
(in a square these are the same distance!)
The total surface area of 6 faces =
6 × area of one square…

4. Example…
Find the surface area of this cube…
2cm

5. Net & Surface Area One square face = 2 × 2 = 4cm²
Total Surface area = 6 faces = 6 x 4 = 24cm²
2cm

6. Cuboids
A cuboid can have all 3 dimensions different BUT there are still 6 faces.
All the faces are rectangles and there are pairs that are the same (front & back / two sides / top and bottom) so you can work out the area of each rectangle and know it’s the same for another one!

7. Example… Find the surface area of this cuboid… 3cm 2cm 5cm TOP RT
FRONT
2cm
5cm

8. Net & Surface Area TOP = 2 × 5 = 10cm² Bottom = same = 10cm²
FRONT = 3 × 5 = 15cm²
Back = same = 15cm²
RIGHT = 3 × 2 = 6cm²
Left = same = 6cm²
Total surface area = = 62cm²
TOP
2cm
FRONT RT
3cm
5cm

9. Did you notice…?
Did you notice that for the cuboid we just had to multiply each of the 3 dimensions together in pairs?
Let’s look at another example…

10. Example 2… Find the surface area of this cuboid… 5cm 3cm 8cm TOP RT
FRONT
3cm
8cm

11. Solution without a net…
Put the 3 dimensions
(3, 5 and 8) into
3 different pairs
and multiply…
3 × 5 = 15cm² (for Right & Left)
3 × 8 = 24cm² (for Top & Bottom)
5 × 8 = 40cm² (for Front & Back)
Add 6 faces together = = 158cm²
3cm
5cm
8cm
FRONT
TOP RT

12. Prisms & Cylinders
Prisms have 2 end shapes. All the other faces are rectangles. For cylinders these end shapes are circles.
There will be as many rectangles as there are edges to the end shape. For cylinders – just one rectangle whose length is the same distance as the circumference of the circle.
Calculate the area of one end shape (and double for both ends) and add to this the area of each of the rectangles.

13. Example… Find the surface area of this L-shaped prism… 5cm 3cm 2cm 7cm
FRONT
TOP
RT1
RT2
RT3
5cm
7cm

14. Net & Surface Area TOP = 3 × 7 = 21cm² LT = 7 × 7 = 49cm²
BASE = 6 × 7 = 42cm²
RT3 = 2 × 7 = cm²
RT2 = 3 × 7 = cm²
RT3 = 5 × 7 = cm²
L-shapes are each 2 rectangles…
FRONT = (3 × 5) + (6 × 2) = 27cm²
BACK = (3 × 5) + (6 × 2) = 27cm²
Total surface area = = 236cm²
FRONT
TOP
BACK LT
BASE
RT3
RT2
RT1
3cm
5cm
2cm
6cm
6cm
2cm
3cm
5cm
7cm

15. What next?
Print out the notes called PAV4-SArea. Read through them and make sure you answer any questions.
Work through the MyMaths lesson and its online homework called Nets, Surface Area found at:
Save and complete the worksheet called SArea-S1.xlsx
Now move on to the PAV5a powerpoint