1. Surface Area: Prisms and Pyramids
Unit Five Lesson 6
Surface Area: Prisms and Pyramids

2. 3 easy steps to calculate the Surface Area of a solid figure
Determine the number of surfaces and the shape of the surfaces of the solid
Apply the relevant formula for the area of each surface
Sum the areas of each surface

3. Surface Area – Basic concept
4 rectangular faces and
2 square faces
Surface Area – Basic concept
rectangle
rectangle
rectangle
square
square
rectangle
Determine the number and shape of the surfaces that make up the solid.
When you’ve done all that find the area of each face and then find the total of the areas.
It might be easier to think of the net of the solid.

4. Four rectangular faces
Square prism
Find the surface area of this figure with square base 5 cm and  height 18 cm
Two square faces
Four rectangular faces
18 cm
5 cm

5. Rectangular prism Now sum these areas 20 cm 15 cm 5 cm
Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm.
Now sum these areas
20 cm
15 cm
5 cm

6. Surface Area of Prisms
The surface area of a prism is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 6 faces to this rectangular prism.
Front and back are the same
Top and Bottom are the same
Two ends are the same.

7. Surface Area of Prisms
To find the surface area, add the areas together.
Top and Bottom
A = bh
A = (90)(130)
A = cm2
Ends
A = bh
A = (90)(50)
A = 4500 cm2
Front and back
A = bh
A = (130)(50)
A = 6500 cm2
Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back)
= 2(11700) + 2(4500) + 2(6500)
= cm2

8. YOU TRY!
To find the surface area, add the areas together.

9. SOLUTION To find the surface area, add the areas together.
Top and Bottom
A = bh
A = (4)(10)
A = 40 m2
Ends
A = bh
A = (2)(4)
A = 8 m2
Front and back
A = bh
A = (2)(10)
A = 20 m2
Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back)
= 2(40) + 2(8) + 2(20)
= 136 m2

10. Triangular Prism 1 2 3 height 8 cm Recall
Find the surface area of this figure with dimensions as marked.
12 cm
10 cm 6 8
height 8 cm
12 cm
20 cm
10 cm
Hence, total surface area
Determine the number of faces and the shape of each face
Recall 1
Apply the area formulae for each face 2
Sum the areas to give the total surface area 3

11. Square Pyramid P height 13 cm. 13 12 10 T
Hence, total surface area
Square Pyramid
Find the surface area of this figure with square base 10 cm and  height 12 cm. 10 13 T P
height 13 cm.
4 triangular faces with the same dimensions and 1 square face
We need to find the  height of each triangular face. 12

12. Surface Area of Triangular Prisms
The surface area of a triangular prism is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 5 faces to this triangular prism.
Two ends are the same.
Three sides depend on the type of triangle:
Equilateral
Isosceles
Scalene

13. Surface Area of Triangular Prisms
To find the surface area, add the areas together.
Bottom
A = bh
A = (1.3)(2.1)
A = 2.73 m2
Ends
A = bh  2
A = (1.3)(0.5)  2
A = m2
Front
A = bh
A = (2.1)(0.5)
A = 1.05 m2
Back
A = bh
A = (2.1)(1.2)
A = 2.52 m2
Total Surface Area = Bottom + 2(Ends) + Front + Back
= (0.325)
= 6.95 m2

14. YOU TRY!
To find the surface area, add the areas together.

15. SOLUTION To find the surface area, add the areas together. Sides
Height = .866
a2 = c2 - b2
a2 = (1)2 - (0.5)2
a2 =
a2 = 0.75
a = 0.866
Sides
A = bh
A = (1)(3)
A = 3 m2
Ends
A = bh  2
A = (1)(0.866)  2
A = m2
Total Surface Area = 2(Ends) + 3(sides)
= 2(0.433) + 3(3)
= m2

16. Surface Area of Pyramids
The surface area of a pyramid is the entire area of the outside of the object.
To calculate surface area, find the area of each side and add them together.
There are 5 faces to this triangular pyramid.
One square bottom
Four triangular sides are the same.

17. Surface Area of Pyramids
To find the surface area, add the areas together.
Bottom
A = s2
A = (4)(4)
A = 16 cm2
sides
A = bh  2
A = (4)(3)  2
A = 6 cm2
Total Surface Area = Bottom + 4(sides)
= (6)
= 40 cm2

18. YOU TRY!
To find the surface area, add the areas together.

19. SOLUTION To find the surface area, add the areas together. Bottom
A = 25 cm2
sides
A = bh  2
A = (5)(6)  2
A = 15 cm2
Total Surface Area = Bottom + 4(sides)
= (15)
= 85 cm2

20. Practice page 178 and 179
Odd #1 - 13