surface area is how much area is on the outside of a solid. we measure surface area with square...
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Surface area is how much area is on the outside of a solid. We measure surface area with square units.
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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
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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
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How do we find the surface area of a
rectangular prism?
10 units 12 units
6 u
nit
s
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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.
+
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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
+
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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.
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How do think we find the surface area of atriangular prism?
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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.
+
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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.
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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.
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End of Surface Area Lesson.
Continue with Volume
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OLUME
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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!)
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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
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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
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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
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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.
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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.
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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)
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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
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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
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THE END