1. SURFACE
AREA

2. Surface area is how much area is on the outside of a solid
Surface area is how much area is on the outside of a solid. We measure surface area with square units.

3. What We Know:
AREA is the amount of space inside a flat surface, which is measured with square units.
Square
Rectangle
Triangle
3 units
3 units
3 units
4 units
4 units
Area = b x h
= 9 square units
Area = b × h
= 12 square units
Area = (b × h) ÷ 2
= 6 square units

4. What We Know:
Surface —On a prism, surfaces refer to the flat faces that make up the solid.
Rectangular prisms
have 6 faces.
All faces are rectangles.
Triangular prisms
have 5 faces.
2 are triangles, 3 are rectangles

5. How do we find the surface area of a rectangular prism?
10 units
12 units
6 units

6. The front and back are identical. The left and right are identical.
10 units
12 units
6 units
We can “unfold” the prism
to make its net.
We can find the area of
each rectangle.
The front and back are identical.
The left and right are identical.
BACK
The top and bottom rectangles are identical
6 units
10 units
BOTTOM
RIGHT
LEFT
Top = u2
Bottom = u2
TOP View
6 × 12 = 72
sq. units
6 × 12 = 72
sq. units
10 × 12 = 120
square units
10 × 12 = 120
square units
12 units
12 units
12 units
12 units
Front = u2
Back = u2 +
6 units
10 units
6 units
10 units
Left Side = u2
Right Side = 72 u2
6 × 10 = 60
square units
6 × 10 = 60
square units
FRONT
6 units
10 units
504 u2

7. To find the surface area of a rectangular prism, you are finding the area of each of the 6 rectangular surfaces and adding them up to get a total.
Top = u2
Bottom = u2
10 units
12 units
6 units
Front = u2
Back = u2 +
Left Side = u2
Right Side = 72 u2
504 u2
Surface Area

8. Find the surface area of this rectangular prism.
Quick
Check!
Find the surface area of this rectangular prism.
Click to reveal the answer.
Front = 9 cm × 12 cm = 108 cm2
Back = Front = 108 cm2
Left Side = 9 cm × 8 cm = 72 cm2
Right Side = Left Side = 72 cm2
Top = 8 cm × 12 cm = 96 cm2
Bottom = Top = 96 cm2
Surface Area = 552 cm2
8 cm
9 cm
12 cm

9. How do think we find the surface area of a triangular prism?

10. + We can find the area of each polygon. We can “unfold” the prism
12 units
10 units
8 units
6 units
We can find the
area of
each polygon.
We can “unfold”
the prism
to make its net.
We add up the
areas of all the
faces.
6 units
8 units
(6 × 8) ÷ 2 =
24 u2
(6 × 8) ÷ 2 =
24 u2
12 units
10 units
12 units
6 units
12 units
10 units
Rectangle 1 = 120 u2
Rectangle 2 = 72 u2
Rectangle 3 = 120 u2
Triangle 1 = u2
Triangle 2 = u2
10 × 12 =
120 u2
6 × 12 =
72 u2
10 × 12 =
120 u2 +
360 u2
8 units

11. Click to reveal the answer.
Quick
Check!
What are the shapes and measurements for each of the faces of this triangular prism? List them.
Click to reveal the answer.
Rectangle 1 = 3 in × 3 in
Rectangle 2 = 3 in × 5 in
Rectangle 3 = 3 in × 4 in
Triangle 1 = 3 in × 4 in
Triangle 2 = 3 in × 4 in
5 inches
4 inches
3 inches
3 inches

12. Now find the surface area of this triangular prism.
Quick
Check!
Now find the surface area of this triangular prism.
Click to reveal the answer.
Rectangle 1 = 3 in × 3 in = 9 in2
Rectangle 2 = 3 in × 5 in = 15 in2
Rectangle 3 = 3 in × 4 in = 12 in2
Triangle 1 = (3 in × 4 in) ÷ 2 = 6 in2
Triangle 2 = (3 in × 4 in) ÷ 2 = 6 in2
Total Surface Area = 48 in2
5 inches
4 inches
3 inches
3 inches

13. End of Surface Area Lesson.
Continue with Volume

14. OLUME

15. What We Need to Understand
Volume is the amount of space inside a three-dimensional object.
In order to measure volume, we need a three-dimensional unit, so we use cubes.
The size of the cube depends on the unit that the object is measured with, so we can measure with cubic inches, cubic feet, cubic centimeters, etc.
A cubic inch is a cube that measures an inch on each of its side; a cubic mile is a cube that measures a mile on each of its sides. (That’s BIG!)

16. 5 units × 5 units = 25 square units Cubes in Bottom Layer × Height
Now we can determine how many LAYERS of these cubes there are in the prism. The number of layers is the same as the prism’s HEIGHT.
To determine the number of cubes that fill this rectangular prism, first we will find out how many cubes will fit in the bottom.
The number of SQUARES that will fill the bottom (base) is the same as the AREA of the base. Since the bottom is a rectangle, we can use LENGTH × WIDTH to determine the number of squares on the base.
If we know how many SQUARES are on the bottom then we could set a cube on each of those squares.
Volume of Rectangular Prisms
5 units
LENGTH × WIDTH
5 units × 5 units = 25 square units
25 squares  25 cubes!
Cubes in Bottom Layer × Height
25 cubes × 5
= 125 cubes
5 units

17. V = L × W × H V = B.A. x H The formula:
Volume of rectangular prism = Base Area × Height
V = B.A. x H
B.A. = AREA of the Base H = Height or distance between the bases
The Base Area (B.A.) for any rectangular prism is
Length × Width
so we can also state the formula for a rectangular prism as:
V = L × W × H
5 units
5 units × 5 units × 5 units = 125 cubic units

18. Let’s find the volume of this rectangular prism by using the formula
B.A. × H
V = B.A. × H
V = (5 × 4) × 20
V = 20 × 20
V = 400 cm3
20 cm
4 cm
5 cm
Remember that our units will always
be in terms of “cubic” units

19. Volume of Rectangular Prism = B.A. x H Click to reveal the answer.
Quick
Check!
A packing box is 20 cm high, 15 cm wide and 18 cm deep. Find the volume.
Volume of Rectangular Prism = B.A. x H
Volume = (15 x 18) x 20
Volume = 270 x 20
Volume = 5400 cm3
Click to reveal the answer.

20. V = B.A. x H Volume of Triangular Prisms
The formula for finding the volume of a triangular prism is the same as our formula for a rectangular prism:
V = B.A. x H
B.A. = AREA of the Base H = Height or distance between the bases
B.A. = 12 units2 (the number of cubes in one layer)
V = B. A. x H
V = 12 units2 × 5 units
V = 60 units3
Then we can multiply that by the height, which is the number of layers.
4 units
6 units
First find the area of the base, which is a triangle:
B.A. = (B x H) ÷ 2
B.A. = (6 × 4) ÷ 2
B.A. = 12 units2
The area of the base tells us how many cubes are in one layer.
5 units

21. CAUTION!!
Don’t be fooled by a triangular prism that is not sitting on its base!
We still need to find the area of the base (the triangle)
and
multiply by the height (the distance between the bases)

22. V = B.A. x H Let’s find the volume of this triangular prism
V = Area of the Base × Height
V = (16 cm × 10 cm ÷ 2) × 15 cm
V = (80 cm2) × 15 cm
V = 1200 cm3
10 cm
15 cm
16 cm
Remember that our units will always
be in terms of “cubic” units
Continue

23. Find the volume of this triangular prism.
Quick
Check!
Mark’s scout group has a pup tent that is the shape of a triangular prism. It is 8 feet long, 6 feet wide and has a height of 5 feet from the ground to the peak of the roof. How many cubic feet of air are inside the tent?
Click to reveal the answer.
Volume = B.A. × H
Volume = (6 ft × 5 ft ÷ 2) × 8 ft
Volume = 120 ft3
6 ft
5 ft
8 ft

24. THE END