1. Slideshow 49, Mathematics Mr Richard Sasaki Room 307
Surface Area
Slideshow 49, Mathematics
Mr Richard Sasaki
Room 307

2. Objectives Review how to find the area of various polygons
Learn how to calculate the surface area of cuboids, triangular prisms and square- based pyramids
Learn how to calculate the surface area of a cylinder

3. Answers 15𝑐 𝑚 2 49𝑐 𝑚 2 8𝑐 𝑚 2 108𝑐 𝑚 2 91𝑐 𝑚 2 70𝑐 𝑚 2 26𝑐 𝑚 2
204𝑐 𝑚 2
135𝑐 𝑚 2

4. Surface Area What is surface area?
The total area of faces & surfaces on a 3D shape.
Calculating surface area for cuboids and triangular prisms is easy as long as we know the dimensions of each face.
3 cm
2 cm
3 cm
3 cm
2 cm
2 cm
5 cm
5 cm

5. Surface Area - Cuboid 3 cm 15 cm2 6 cm2 10 cm2 6 cm2 2 cm 3 cm 15 cm2
All we do is add the total area of each face.
We just simply add the numbers together.
= 10∙2+15∙2+6∙2 =
= 62𝑐 𝑚 2

6. Surface Area – Triangular Prism
Visualising a net is always good!
3 cm
4 cm
5 cm
10 cm
3 cm
3 cm
4 cm
5 cm
4 cm
10 cm
Surface Area:
10∙4 +
10∙3 +
10∙5 +
0.5∙4∙3 ∙ 2
= 40+
30+
50+ 12
= 132𝑐 𝑚 2

7. Answers
14𝑐 𝑚 2
216𝑐 𝑚 2
168𝑐 𝑚 2
156𝑐 𝑚 2
252𝑐 𝑚 2
270𝑐 𝑚 2

8. Square-Based Pyramids
Let’s have a look at the square based pyramid. 𝑠 𝑠 𝑎 𝑎 𝑎 𝑎
This should be easy to calculate the surface area with too!

9. Square-Based Pyramids
Example
7 𝑐𝑚
7 𝑐𝑚
4 𝑐𝑚
4 𝑐𝑚
4∙7∙ 1 2 ∙4
Surface area =
4 2 +
=16+56
=72 𝑐 𝑚 2

10. Cylinders
Let’s calculate the surface area of a cylinder with its radius and length.
Example
We know the cylinder is made of two and, if flattened a .
circles
rectangle 𝑙
=10𝑚 𝑟
=2𝑚
𝐶=2𝜋𝑟
4𝜋 𝑚 2𝑚
10𝑚

11. Cylinders S.A = 2∙𝜋 𝑟 2 + 2𝜋𝑟𝑙 𝐶=2𝜋𝑟 =2∙𝜋∙ 2 2 +2𝜋∙2∙10 4𝜋 𝑚 2𝑚
=8𝜋+40𝜋
10𝑚
=48𝜋 𝑚 2
On your test you won’t receive any formulae for surface area as the calculations are somewhat obvious but you are welcome to remember some if you need to!

12. Answers
40𝑐 𝑚 2
45 𝑚 2
161𝑚 𝑚 2
56𝑐 𝑚 2
105 𝑘𝑚 2
1035𝑘 𝑚 2

13. Answers
152𝜋 𝑐 𝑚 2
84 𝜋 𝑚 2
48𝜋 𝑐 𝑚 2
3.5𝜋 𝑚 2
480𝜋 𝑚 𝑚 2
16 𝜋 𝑘 𝑚 2