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

What We Know: AREA is the amount of space inside a flat surface, which is measured with square units.

3 units

Area = b x h= 9 square units

4 units

3 units

Area = b × h= 12 square units

4 units

3 units

Area = (b × h) ÷ 2= 6 square units

Square Rectangle Triangle

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

How do we find the surface area of a

rectangular prism?

10 units 12 units

6 u

nit

s

10 units 12 units

6 u

nit

s

10 units

12 u

nit

s

6 units 6 units 10 units

12 u

nit

s

12 u

nit

s

12 u

nit

s

6 u

nit

s6

un

its

10 units

10 units

TOP View

10 × 12 = 120

square units

10 × 12 = 120

square units

BOTTOMTop = 120 u2

Bottom = 120 u2

Front = 60 u2

Back = 60 u2

Left Side = 72 u2

Right Side = 72 u2

504 u2

FRONT

BACK

6 × 10 = 60square units6 × 10 = 60

square units

LEFT6 × 12 =

72sq.

units

6 × 12 =72sq.

units

RIGHT

We can “unfold” the prism to make its net.

We can find the area of each rectangle.

The top and bottomrectangles are identical

The front and backare identical. The left

andright are identical.

+

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 = 120 u2

Bottom = 120 u2

Front = 60 u2

Back = 60 u2

Left Side = 72 u2

Right Side = 72 u2

504 u2

Surface Area

+

Find the surface area of this rectangular prism.

12 cm

8 cm

9 cm

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

Click to reveal the answer.

How do think we find the surface area of atriangular prism?

12 units

10 u

nits

8 u

nit

s

6 units

10 un

its

12 u

nit

s6 units

12 u

nit

s

10 units

12 u

nit

s

10 units

6 units

8 u

nit

s8

un

its

We can “unfold” the prism

to make its net.

We can find the area of

each polygon.

10 × 12 =120 u2

6 × 12 =72 u2

10 × 12 =120 u2

(6 × 8) ÷ 2 =24 u2

(6 × 8) ÷ 2 =24 u2

Rectangle 1 = 120 u2

Rectangle 2 = 72 u2

Rectangle 3 = 120 u2

Triangle 1 = 24 u2

Triangle 2 = 24 u2

360 u2

We add up theareas of all the

faces.

+

What are the shapes and measurements for each of the faces of this triangular

prism? List them.

3 inches

3 in

ches4

inch

es

5 inches

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

Click to reveal the answer.

Now find the surface area of this triangular prism.

3 inches

3 in

ches4

inch

es

5 inches

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

Click to reveal the answer.

End of Surface Area Lesson.

Continue with Volume

OLUME

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!)

To determine the number of cubesthat fill this rectangular prism, firstwe will find out how many cubeswill fit in the bottom.

If we know how many SQUARESare on the bottom then we could set a cube on each of those squares.

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.

5 units

5 units

LENGTH × WIDTH

5 units × 5 units = 25 square units

25 squares 25 cubes!

Now we can determine how manyLAYERS of these cubes there are inthe prism. The number of layers is the same as the prism’s HEIGHT.

5 unitsCubes in Bottom Layer × Height

25 cubes × 5

= 125 cubes

Volume of Rectangular Prisms

The formula:

5 units × 5 units × 5 units = 125 cubic units

5 units

5 units

5 units

Volume of rectangular prism = Base Area × Height

V = B.A. x HB.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

4 cm5 cm

20 cm

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

Remember that our units will always

be in terms of “cubic” units

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.

A packing box is 20 cm high, 15 cm wide and 18 cm deep.

Find the volume.

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

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

4 units 6 units

The area of the base tells us how many cubes are in one

layer. 5 units

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.

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)

16 cm

15 c

m

Continue

Let’s find the volume of this triangular prism

V = B.A. x H

V = Area of the Base × Height

V = (16 cm × 10 cm ÷ 2) × 15 cm

V = (80 cm2) × 15 cm

V = 1200 cm3

Remember that our units will always

be in terms of “cubic” units

10 c

m

Find the volume of this triangular prism.

Volume = B.A. × H

Volume = (6 ft × 5 ft ÷ 2) × 8 ft

Volume = 120 ft3

Click to reveal the answer.

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?

8 ft6 ft

5 ft

THE END