1. Surface Area and Volume of
Prisms part 1

2. Prism — SA = sum of areas of all faces (bases included)
Cylinder — SA = sum of areas of bases and lateral surface area
Prism — SA = sum of areas of all faces (bases included)
Pyramid — SA = sum of areas of all faces (bases included)

3. Lateral Area of a Prism
The lateral area of a prism is the sum of the areas of the lateral faces.
Lateral Face—a lateral face of a prism is a face that joins the bases of the prism
The lateral area of the prism is the total area of its lateral faces.

4. Lateral Area of a Prism
Suppose the perimeter of the base is p and the height is h.

5. Lateral Area of a Prism
You can unfold a prism to form a net rectangle.

6. Lateral Area of a Prism
Notice that the perimeter of the base of the prism is equal to the base of the rectangle and that the heights are the same.

7. Lateral Area of a Prism
The lateral area of the prism and the area of the rectangle are equal.
So the lateral area of the prism equals the base of the rectangle times the height of the rectangle.
Lateral Area = perimeter of base · height of prism

8. Lateral Area of a Prism
Remember the base of the rectangle equals the perimeter of the base of the prism and the height of the rectangle is the same as the height of the prism.
So the lateral area of the prism equals the perimeter of its base p times its height h.
L.A. = P*h

9. Surface Area of Prism
The surface area of a prism is the sum of the lateral area and the areas of its bases.
The surface area of a prism equals the lateral area plus two times the area of a base.
Surface Area = Lateral Area + 2 · area of a base
Or, SA = LA + 2B

10. Surface Area of a Cube
The surface area of a cube is the sum of the areas of the faces of the cube.
Suppose you have a cube with side length s.
Each face of the cube is a square.
The area of a square is the side length squared.

11. Part 1 Example 1
Find the surface area of each rectangular prism.

12. Part 1 Example 1
Find the surface area of each rectangular prism.

13. Part 2 Example 1
Ms. Adventure went on a trip around the world. In the Netherlands, she tasted Dutch cheese. The piece of cheese has the shape of a triangular prism. How much surface area is there for mold to grow on?

14. Part 2 Example 2
What is the surface area of the triangular prism?

15. Part 3 Example 1
When a base of a prism is a regular polygon, you can decompose the polygon to find its area.
You can decompose a regular hexagon into 6 equilateral triangles.
The 6 triangles are the same size.
After you find the area of 1 triangle, you can multiply the area by 6 to find the area of the entire hexagon.

16. Part 3 Example 2
Ms. Adventure wants to make a box like one she saw in Japan. She plans to cover the box with paper. The box has the shape of a regular hexagonal prism. To the nearest square inch, how much paper does Ms. Adventure need to cover the box?

17. Part 3 Example 3
To the nearest square inch, what is the surface area of the regular hexagonal prism?

18. Homework:
Surface Area of Prisms Worksheet

19. Area of the base x height = (length x width) x height
Volume of a Prism
Notice that the area of the base of the prism is 20 square units and that the height of the prism is 3 units.
So the formula for the volume of a prism equals the area of the base times the height.
Or, V = Bh
Area of the base x height = (length x width) x height

20. V = area of base · height Find the Volume of the Prism. V = Bh
V = 54 ft³

21. Find the Volume of the Prism.
V = side length cubed
V = s³
V = (3)³
V = (3) (3) (3)
V = 27 ft³

22. V = area of base · height Find the Volume of the Prism. V = Bh
V = 54 ft³

23. What is the volume of a cube with edge length ¾ ft.?
Find the Volume of each Prism.
What is the volume of a cube with edge length ¾ ft.?
V = side length cubed
V = s³
V = ( 3/4 )³
V = ( 3/4 ) ( 3/4 ) ( 3/4 )
V = 27/64 ft³

24. Find the Volume the Prism.
V = area of base · height
V = Bh
V = ( 1/2 bh)*h
V = ( 1/2 ) (12) (5) (17)
V = 510 units³

25. Find the Volume of each Prism.
V = area of base · height
V = Bh
V = ( 1/2 bh) h
V = ( 1/2 ) (4) (3.5) (11.6)
V = 81.2 m³

26. Find the Volume of the Prism
Ms. Adventure’s Japanese box has the shape of a regular hexagonal prism. To the nearest cubic inch, what is the amount of space inside the box?
V = area of base · height
V = Bh
V = 6 ( 1/2 bh)h or (3bh)(h)
V = (6)( 1/2 )(2.6)(3)(4) or (3)(2.6)(3)(4)
V = 93.6 in³
V= 94 in³

27. Find the Volume of the Prism
V = area of base · height
V = Bh
V = 6( 1/2 bh)h or (3bh)(h)
V = (6)( 1/2 )(6)(5.2)(10.9) or (3)(6)(5.2)(10.9)
V = cm³

28. Volume of Prisms Worksheet
HW: