Section 10.1
Areas of Parallelograms and Triangles
Area of a Rectanile:
The area of a rectangle is the product of its base and height.
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Base ofa Parallelogram: j
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Corresponding Altitude
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Height:
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Area of a Parallelogram:
The area of a parallelogram is the product of a base and the corresponding height.
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Example 1: Finding the Area of a Parallelogram
Find the area of each parallelogram.
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Example 2: Finding a Missing Dimension
For parallelogram ABCD, find CF to the nearest tenth.
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Base of a Triangle:
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Corresponding height:
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Area of a Triangle:
The area of a triangle is half the product of a base and the corresponding height.
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Example 3: Finding the Area of a Triangle
Find the area of the triangle.
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Section 10.2
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Areas of Trapezoids, Rhombuses, and Kites
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Bases of a Trapezoid:
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Height of a Trapezoid:Th
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Area of a Trapezoid:
The area of a trapezoid is half the product of the height and the sum of the bases.
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Example 1: Real-World Connection
Approximate the area of Arkansas by finding the area of the trapezoid shown.
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Example 2: Finding Area Using a Right Triangle
What is the area of trapezoid PQRS?
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Area of a Rhombus or a Kite:
The area of a rhombus or a kite is half the product of the lengths of its diagonals.
Example 3: Finding the Area of a Kite
Find the area of kite KLMN.
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Example 4: Finding the Area of a Rhombus
Find the area of rhombus ABCD.
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Section 10.3
Regular Polygon:
4pothem:
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Areas of ReuIar Po1yons
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Perimeter:
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Area of a Regular Polygon:
The area of a regular polygon is half the product of the apothem and the perimeter.
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Example 1: Finding the Area of a Regular Polygon
Find the area of a regular decagon with a 12.3-in. apothem and 8-in, sides.
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Example 2: Finding the Area of a Regular Polygon
Find the area of the regular hexagon. Leave your answer in simplest radical form.
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Example’4 Finding the Area of a Regular Polygon
Find the area of a regular hexagon with a side length of 1 6ft. Leave your answer in
simplest radical form.
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Section 10.6
Circle:
Circles and Arcs
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Radius: p
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Diameter: ---hr
Central Angle:
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Congruent Circles:
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Name the following using the circle below.
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The circle:
The center:
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The radius:
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The Diameter:
Two central angles:
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Example 1: Naming Parts of a Circle
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Example 2: Real-World Connection
To learn how people really spend their time, a research firm studied the hour-by-hour
activities of 3600 people. The participants were between 18 and 90 years old. Each
participant was sent a 24-hour recording sheet every March for three years from 2000 to
2002.
Some information from the study is shown in this circle graph. What is the measure, in
degrees, of the central angle used for each part?
Sleep:
Other:
Sleep
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Entertainment:
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Must Do:
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Work:
Food:
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Minor Arc:
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Major Arc:
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c. The major arcs that contain point A.
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Identify the following in circle 0.
a. The mmor arcs:
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Example 3: Indentifying Arcs
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Semicircle:
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Adjacent Arcs:
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Arc Addition Postulate:
The measure of the arc formed by two adjacent arcs is the sum of the measures of the
two arcs.
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Example 4: Finding the Measures of Arcs
Find the measure of each arc.
a.
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c.
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Circumference:
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Circumference of a Circle:
The circumference of a circle is r times the diameter.
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Concentric Circles:
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Example 5: Real-World Connection
A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In
completing the outer turning circle, how much further does a tire travel than a tire on the
concentric inner circle?
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Arc Length:
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Arc Length Theorem:
The length of an arc of a circle is the product of the ratio measure of the arc and the
360
circumference of the circle.
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Example 6: Finding Arc Length
Find the length of each arc. Leave your answer in terms of r.
b. Find XPY
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Congruent Arcs:
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Section 10.7
Areas of Circles and Sectors
Area of a Circle:
The area of a circle is the product of
and the square of the radius.
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Example 1: Real-World Connection
How much more pizza is
in a 1 2-in.-diameter pizza than in a 10-in, pizza?
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Area of a Sector of a Circle:
The area of a sector of a circle is the product of the ratio measure of the arc and the
360
area of the circle.
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Example 2: Finding the Area of a Sector of a Circle
Find the area of sector ZOM. Leave your answer in terms of n-.
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Segment of a Circle:
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Area of a Segment:
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Example 3: Finding the Area of a Segment of a Circle
Find the area of the shaded segment. Round your answer to the nearest tenth.
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