Section A Area
8-1
8-3
8-4
8-5
Converting Customary Units
Area of Rectangles and Parallelograms
Area of Triangles and Trapezoids
Area of Composite Figures
Section A Quiz
Section B Volume and Surface Area
8-6
8-7
Volume of Prisms
Surface Area
Section B Quiz
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LESSON
8-1
Measurement and Geometry
Converting Customary Units
Objective
To convert customary units of measure
You can use the information in the table below to convert one customary unit to
another.
Length
1 foot = 12 inches
1 yard = 36 inches
1 yard = 3 feet
1 mile = 5,280 feet
1 mile = 1,760 yards
Example 1
Common Customary Measurements
Weight
Capacity
1 pound = 16 ounces
1 cup = 8 fluid ounces
1 ton = 2,000 pounds
1 pint = 2 cups
1 quart = 2 pints
1 quart = 4 cups
1 gallon = 4 quarts
1 gallon = 16 cups
1 gallon = 128 fluid ounces
Using a Conversion Factor
A. Convert 93 inches to feet.
Set up a conversion factor.
Think: inches to feet – 1 ft = 12 in., so use
1 ft
12 in.
Multiply 93 in. by the conversion factor.
93 in.
1 ft
12 in.
***Write the unit you are converting to in
93 in. 1 ft
1
12 in.
the numerator and the unit you are converting
from in the denominator.
B. Convert 2 pounds to ounces.
1
93 ft
12
7.75 ft
Example 2
Converting Units of Measure by Using Proportions
Convert 48 quarts to gallons.
1 gallon is 4 quarts. Write a proportion.
Use a variable for the value you are
4 qt
1 gal
trying to find.
The cross products are equal.
Divide each side by 4 to undo the
multiplication.
48 qt
x gal
4 • x = 1 • 48
4x = 48
x = 12
48 qt = 12 gal
Example 3
Problem Solving Application
The Washington Monument is about 185 yards tall. This height is almost equal to the length
of two football fields. How many feet is this?
Homework:
p. 344-345: 1-13 odd, 14-26 even, 38,
45, 47
2
LESSON
8-3
Measurement and Geometry
Area of Rectangles and Parallelograms
Objective
To find the area of rectangles and parallelograms
Vocabulary
area _________________________________________________________________
Example 2
Finding the Area of a Rectangle
Find the area of the rectangle.
Write the formula.
A = lw
Substitute ____ for l and ____ for w.
A = ___ • ___
Multiply.
A = ________
The area is ______m2.
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You can use the formula for the area of a rectangle to write a formula for the area of a parallelogram.
Imagine cutting off the triangle drawn in the parallelogram and sliding it to the right to form a
rectangle.
The area of a parallelogram = bh
The area of a rectangle = lw
The base of the parallelogram is the length of the rectangle.
The height of the parallelogram is the width of the rectangle.
Example 3
Finding the Area of a Parallelogram
Find the area of the parallelogram.
Write the formula.
A = bh
Substitute ____ for b and ____ for h.
A = ___ • ___
Multiply.
A = ________
A = ________
The area is _____ in2.
Example 4
Recreation Application
A rectangular park is made up of a rectangular
spring-fed pool and a limestone picnic ground
that surrounds it. The rectangular park is 30 yd
by 25 yd, and the pool is 10 yd by 4 yd. What is
the area of the limestone picnic ground?
To find the area of the picnic ground, subtract the area
of the pool from the area of the park.
park area
–
pool area
=
picnic ground area
Homework:
p. 352: 4-10, 14-20
4
LESSON
8-4
Measurement and Geometry
Area of Triangles and Trapezoids
Objective
To find the area of triangles and trapezoids
You can divide any parallelogram into two congruent triangles. The area of each triangle is half the
area of the parallelogram.
Example 1
Finding the Area of a Triangle
Find the area of each triangle.
Write the formula.
Substitute ____ for b and ____ for h.
Multiply.
The area is ______ cm2.
The area is _______ yd2.
5
1
bh
2
1
A = (___ • ___)
2
1
A = (________)
2
A = ________
A=
Example 2
Architecture Application
The diagram shows the outline of the foundation of the
Flatiron Building. What is the area of the foundation?
You can divide a parallelogram into two congruent trapezoids. The area of each trapezoid is half the
area of the parallelogram.
Example 3
Finding the Area of a Trapezoid
Find the area of the trapezoid.
Write the formula.
1
h(b1 + b2)
2
1
A = (___)(___+___)
2
1
A = (___)(___)
2
A = ________
A=
Substitute ____ for h,____ for b1, and ____ for b2
Multiply.
The area is ______ m2.
Homework:
p. 358: 1-16
6
LESSON
8-5
Measurement and Geometry
Area of Composite Figures
Objective
To break a polygon into simpler parts to find its area
You can find the areas of irregular polygons by breaking them apart into rectangles, parallelograms,
and triangles.
Example 1
Finding the Area of a Composite Figures
Find the area of each polygon.
Think: Break the polygon into rectangles.
Find the area of each rectangle.
A = lw
A = lw
Write the formula for the area of each rectangle.
Add to find the total area.
The area of the polygon is __________.
Think: Break the figure apart into a triangle and
a rectangle.
Find the area of each polygon.
A = lw
A=
1
bh
2
Write the formula for each polygon.
Add to find the total area of the figure.
The area of the figure is ____________.
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LESSON
8-5
Measurement and Geometry
Homework: Area of Composite Figures
Find the area of each polygon.
1.
2.
_______________________________________
3.
________________________________________
4.
_______________________________________
5.
________________________________________
6.
_______________________________________
7.
________________________________________
8.
_______________________________________
________________________________________
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LESSON
8-6
Measurement and Geometry
Volume of Prisms
Objective
To find the volumes of rectangular prisms and triangular prisms
Vocabulary
volume_______________________________________________________________
_____________________________________________________________________
Example 1
Finding the Volume of a Rectangular Prism
Find the volume of the rectangular prism.
Write the formula.
V = lwh
Substitute ____ for l, ____ for h, and ____
for w.
V = ____•____•____
Multiply.
V = ____________
To find the volume of any prism, you can use the formula V = Bh, where B is the area of the base,
and h is the prism’s height.
Example 2
Finding the Volume of a Triangular Prism
Find the area of each triangular prism.
Write the formula.
V = Bh
1
V = ( bh)h
2
Substitute ____ for b, ____ for h, and ____
1
____•____•____
2
for h.
V=
Multiply.
V = ____________
Homework:
p. 370: 1-6, 8-13, 18-20
9
LESSON
8-7
Measurement and Geometry
Surface Area
Objective
To find the surface areas of prisms, pyramids, and cylinders
Vocabulary
surface area __________________________________________________________
_____________________________________________________________________
net __________________________________________________________________
_____________________________________________________________________
Example 1
Finding the Surface Area of a Prism
Find the surface area of each prism.
A. Method 1: Use a net.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face.
A:
B:
C:
D:
E:
F:
A = ___ × ___ = ____
A = ___ × ___ = ____
A = ___ × ___ = ____
A = ___ × ___ = ____
A = ___ × ___ = ____
A = ___ × ___ = ____
S = ____ + ____ + ____ + ____ + ____ + ____ = _________
Add the areas of each face.
B. Method 2: Use a three-dimensional drawing.
Find the area of the front, top, and side and multiply each by 2 to
include the opposite faces.
Front: ____ × ____ = ____ × 2 = ____
Top: ____ × ____ = ____ × 2 = ____
Side: ____ × ____ = ____ × 2 = ____
S = ____ + ____ + ____ = __________
Add the areas of the faces.
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The surface area of a pyramid equals the sum of the area of the base and areas of the triangular
faces.
Example 2
Finding the Surface Area of a Pyramid
Find the surface area of the pyramid
S = area of rectangle + 4 × (area of triangular face)
S = lw + 4 × (
1
bh)
2
S = ___ × ___ + 4 × (
1
× ___ × ___)
2
Substitute.
S = ___ + ___ × ___
S = ____
The surface area is _____________.
Homework:
pp. 376-377: 1-6, 10-15, 20
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