Surface Area
Learning Goals
By the end of the lesson I will be able to:
Rectangular Prisms
How many sides on a rectangular prism?
6, all of which are rectangles
What does it look like unfolded?
Surface Area
Find the surface area by adding up the area of all 6 sides.
There are:
2, 6 cm x 5 cm rectangles
= 30 cm2
2, 15 cm x 6 cm rectangles
= 90 cm2
2, 15 cm x 5 cm rectangles
= 75 cm2
So, 2 x 30 + 2 x 90 + 2 x 75
= 390 cm2
5 cm
15 cm
6 cm
6 cm
6 cm
5 cm
5 cm
15 cm
15 cm
15 cm
15 cm
6 cm
6 cm
5 cm
5 cm
Triangular Prisms
How many sides on a triangular prism?
5: Two triangles and 3 rectangles
What does it look like unfolded?
Surface Area
Find the surface area by adding up the area of all 5 sides.
There are:
2, 5 cm x 10 cm rectangles
= 50 cm2
1, 6 cm x 10 cm rectangle
= 60 cm2
2, base 6, height 4 triangles
= 12 cm2
So, 2 x 50 + 1 x 60 + 2 x 12
= 184 cm2
6 cm
10 cm
5 cm
5 cm
5 cm
6 cm
10 cm
5 cm
5 cm
5 cm
10 cm
10 cm
10 cm
6 cm
5 cm
5 cm
6 cm
h
h2 = 52 - 32
h2 = 25 - 9
h2 = 16
h = 4
Square Based Pyramid
How many sides on a square based pyramid?
5: 4 triangles and 1 square
What does it look like unfolded?
Surface Area
Find the surface area by adding up the area of all 5 sides.
There are:
4, base 4, height 10.2 triangles
= 20.4 cm2
1, 4 cm x 4 cm square
= 16 cm2
So, 4 x 20.4 + 1 x 16
= 97.6 cm2
10 cm
10.2 cm
10.2 cm
4 cm
10 cm
2 cm
10.2 cm
4 cm
Cylinder
How many sides on a cylinder?
3, Two circles and a rectangle
What does it look like unfolded?
Surface Area
Find the surface area by adding up the area of all 3 sides.
There are:
2, circles with radius 3
= 28.27 cm2
1, 7 cm x 18.85 cm rectangle
= 131.95 cm2
So, 2 x 28.27 + 1 x 131.95
= 188.49 cm2
C = 2πr
= 2 x 3.14 x 3
= 18.85
7 cm
3 cm
7 cm
3 cm
3 cm
18.85 cm
Formulae
Not all of the surface areas have easy to remember formulas, but the two that do are:
Rectangular Prism: SA = 2(LW + LH + WH)
Cylinder: SA = 2πr2 + 2πrh