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 ID: 749244
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Slide1
SURFACE
AREASlide2
Surface area
is how much area is on the
outside
of a solid. We measure surface area with square units. Slide3
What We Know:
AREA is the amount of space inside a flat surface, which is measured with square units.
3 units
Area
=
s
2
= 9 square units
4 units
3 units
Area
=
l × w
= 12 square units4 units
3 unitsArea = ½ b × h= 6 square units
Square
Rectangle
TriangleSlide4
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 rectanglesSlide5
How do we find the surface area of arectangular prism?
10 units
12 units
6 unitsSlide6
10 units
12 units
6 units
10 units
12 units
6 units
6 units
10 units
12 units
12 units
12 units
6 units
6 units
10 units
10 unitsTOP View
10 × 12 = 120
square units
10 × 12 = 120
square units
BOTTOM
Top = 120 u
2
Bottom = 120 u
2
Front = 60 u
2
Back = 60 u
2
Left Side = 72 u
2
Right Side = 72 u
2
504
u
2
FRONT
BACK
6 × 10 = 60
square units
6 × 10 = 60
square units
LEFT
6 × 12 =
72
sq. units
6 × 12 =
72
sq. units
RIGHT
We can “unfold” the prism
to make its
net
.
We can find the
area
of
each rectangle.
The top and bottom
rectangles are identical
The front and back
are identical.
The left
and
right are
identical.Slide7
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 u2Bottom = 120 u2
Front = 60 u2
Back = 60 u2
Left Side = 72 u
2Right Side = 72 u2
504
u
2
Surface Area
10 units
12 units
6 unitsSlide8
Find the surface area of this rectangular prism.
QuickCheck!
12 cm
8 cm
9 cm
Front = 9 cm × 12 cm = 108 cm
2Back = Front = 108 cm2
Left Side = 9 cm × 8 cm = 72 cm2Right Side = Left Side = 72 cm
2Top = 8 cm × 12 cm = 96 cm2
Bottom = Top = 96 cm2 Surface Area = 552 cm
2Click to reveal the answer.Slide9
How do think we find the
surface area of a
triangular prism?Slide10
12 units
10 units
8 units
6 units
10 units
12 units
6 units
12 units
10 units
12 units
10 units
6 units
8 units
8 units
We can “unfold”
the prism
to make its net. We can find the area of each polygon.
10 × 12 =120 u2
6 × 12 =72 u210 × 12 =120 u2
½ × 6 × 8 =24 u2
½ × 6 × 8 =24 u2Rectangle 1 = 120 u2Rectangle 2 = 72 u2Rectangle 3 = 120 u
2
Triangle 1 = 24 u
2
Triangle 2 = 24 u
2
360
u
2
We add up the
areas
of all the
faces.
Slide11
What are the shapes and measurements for each of the faces of this triangular prism? List them.
QuickCheck!
3 inches
3 inches
4 inches
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.Slide12
Now find the surface area of this triangular prism.
QuickCheck!
3 inches
3 inches
4 inches
5 inches
Rectangle 1 = 3 in × 3 in = 9 in
2
Rectangle 2 = 3 in × 5 in = 15 in
2
Rectangle 3 = 3 in × 4 in = 12 in
2 Triangle 1 = 3 in × 4 in = 6 in2 Triangle 2 = 3 in × 4 in = 6 in
2 Total Surface Area = 48 in2Click to reveal the answer.Slide13
End of Surface Area Lesson. Continue with Volume Slide14
OLUMESlide15
What We Need to UnderstandVolume 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!) Slide16
To determine the number of cubes
that fill this rectangular prism, first
we will find out how many cubes
will fit in the bottom.
If we know how many SQUARES
are 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 many
LAYERS of these cubes there are in
the prism. The number of layers is
the same as the prism’s HEIGHT.
5 units
Cubes in Bottom Layer × Height
25 cubes × 5
= 125 cubes
Volume of Rectangular PrismsSlide17
The formula:
5 units × 5 units × 5 units =
125 cubic units
5 units
5 units
5 units
Volume of rectangular prism = AREA of the Base × height
V = Bh
B
=
AREA of the Base
h
=
height
or
distance between the bases
The area of the base (B) for any rectangular prism is length × width, so we can also state the formula for a rectangular prism as:
V = l × w × hSlide18
4 cm
5 cm20 cm
Let’s find the volume of this rectangular prism by using the formula l × w × h
V = l × w × h
V = 5 cm × 4 cm × 20 cm
V = (5 × 4 × 20) cm
3V = 400 cm
3
Remember that our units will always be in terms of “cubic” unitsSlide19
Quick
Check!
Volume of Rectangular Prism = l × w × h Volume = 20 cm × 15 cm × 18 cm
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. Slide20
Volume of Triangular Prisms
The formula for finding the volume of a triangular prism is the same as our first formula for a rectangular prism:
V = Bh
B
=
AREA of the base
h
=
height
or
distance between the bases
First find the area of the base, which is a triangle:
B = ½ bh
B = ½ × 6 × 4
B = 12 units
2
4 units
6 units
The area of the base tells us how many cubes are in one layer.
5 units
B = 12 units
2
(the number of cubes in one layer)
V = Bh
V = 12 units
2
× 5 units
V = 60 units
3
Then we can multiply that by the height, which is the number of layers.Slide21
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
)Slide22
16 in
15 inContinueLet’s find the volume of this triangular prism
V = Bh
V = Area of the base × heightV = (½ × 16 in × 10 in) × 15 inV = (80 in
2) × 15 inV = 1200 in
3
Remember that our units will always be in terms of “cubic” units
10 inSlide23
Find the volume of this triangular prism.
QuickCheck!
Volume = B × h
Volume = ½ (6 ft × 5 ft) × 8 ftVolume = 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 ft
6 ft
5 ftSlide24
End of lesson