Splash Screen

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Splash Screen
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Lesson Menu
Five-Minute Check (over Lesson 113) NGSSS Then/No
w New Vocabulary Example 1 Identify Segments
and Angles in Regular Polygons Example 2
Real-World Example Area of a Regular Polygon Key
Concept Area of a Regular Polygon Example 3
Use the Formula for the Area of a Regular
Polygon Example 4 Find the Area of a Composite
Figure by Adding Example 5 Find the Area of a
Composite Figure by Subtracting
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5-Minute Check 1
Find the area of the circle.Round to the nearest
tenth.
A. 37.7 ft2 B. 75.4 ft2 C. 223.6 ft2 D. 452.4 ft2

1. A
2. B
3. C
4. D

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5-Minute Check 2
Find the area of the sector.Round to the nearest
tenth.
A. 25.1 m2 B. 28.3 m2 C. 33.4 m2 D. 50.2 m2

1. A
2. B
3. C
4. D

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5-Minute Check 3
Find the area of the sector.Round to the nearest
tenth.
A. 506.8 in2 B. 570.2 in2 C. 760.3 in3 D. 1520.5
in2

1. A
2. B
3. C
4. D

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5-Minute Check 4
Find the area of the shaded region. Assume that
the polygon is regular. Round to the nearest
tenth.
A. 36.4 units2 B. 39.1 units2 C. 47.3
units2 D. 51.4 units2

1. A
2. B
3. C
4. D

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5-Minute Check 5
Find the area of the shaded region. Assume that
the polygon is regular. Round to the nearest
tenth.
A. 82.5 units2 B. 87.3 units2 C. 92.5
units2 D. 106.7 units2

1. A
2. B
3. C
4. D

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5-Minute Check 6
The area of a circle is 804.2 square centimeters.
The area of a sector of the circle is 268.1
square centimeters. What is the measure of the
central angle that defines the sector?
A. 110 B. 120 C. 135 D. 150

1. A
2. B
3. C
4. D

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NGSSS
MA.912.G.2.5 Explain the derivation and apply
formulas for perimeter and area of polygons.
MA.912.G.2.6 Use coordinate geometry to prove
properties of congruent, regular and similar
polygons, and to perform transformations in the
plane. Also addresses MA.912.G.2.7.
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Then/Now
You used inscribed and circumscribed figures and
found the areas of circles. (Lessons 101and
113)

• Find areas of regular polygons.

• Find areas of composite figures.

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Vocabulary

• center of a regular polygon
• radius of a regular polygon
• apothem
• central angle of a regular polygon
• composite figure

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Example 1
Identify Segments and Angles in Regular Polygons
center point X
central angle ?RXQ
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Example 1
Identify Segments and Angles in Regular Polygons
Answer m?RXQ 72
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Example 1
A. m?DGH 45 B. m?DGC 60 C. m?CGD 72
D. m?GHD 90

1. A
2. B
3. C
4. D

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Example 2
Area of a Regular Polygon
FURNITURE The top of the table shown is a
regular hexagon with a side length of 3 feet and
an apothem of 1.7 feet. What is the area of the
tabletop to the nearest tenth?
Step 1 Since the polygon has 6 sides, the
polygon can be divided into 6 congruent
isosceles triangles, each with a base of 3 ft
and a height of 1.7 ft.
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Example 2
Area of a Regular Polygon
Step 2 Find the area of one triangle.
Area of a triangle
b 3 and h 1.7
2.55 ft2
Simplify.
Step 3 Multiply the area of one triangle by the
total number of triangles.
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Example 2
Area of a Regular Polygon
Since there are 6 triangles, the area of the
table is 2.55 ? 6 or 15.3 ft2.
Answer 15.3 ft2
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Example 2
UMBRELLA The top of an umbrella shown is a
regular hexagon with a side length of 2 feet and
an apothem of 1.5 feet. What is the area of the
entire umbrella to the nearest tenth?

1. A
2. B
3. C
4. D

A. 6 ft2 B. 7 ft2 C. 8 ft2 D. 9 ft2
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Concept
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Example 3A
Use the Formula for the Area of a Regular Polygon
A. Find the area of the regular hexagon. Round to
the nearest tenth.
Step 1 Find the measure of a central angle.
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Example 3A
Use the Formula for the Area of a Regular Polygon
Step 2 Find the apothem.
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Example 3A
Use the Formula for the Area of a Regular Polygon
Step 3 Use the apothem and side length to find
the area.
65.0 m2 Use a calculator.
Answer about 65.0 m2
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Example 3B
Use the Formula for the Area of a Regular Polygon
B. Find the area of the regular pentagon. Round
to the nearest tenth.
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Example 3B
Use the Formula for the Area of a Regular Polygon
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Example 3B
Use the Formula for the Area of a Regular Polygon
a 9 cos 36 and P 10(9 sin 36)
Use a calculator.
Answer 192.6 cm2
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Example 3
A. Find the area of the regular hexagon. Round to
the nearest tenth.
A. 73.1 m2 B. 96.5 m2 C. 126.8 m2 D. 146.1 m2

1. A
2. B
3. C
4. D

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Example 3
B. Find the area of the regular pentagon. Round
to the nearest tenth.
A. 116.5 m2 B. 124.5 m2 C. 138.9 m2 D. 143.1 m2

1. A
2. B
3. C
4. D

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Example 4
Find the Area of a Composite Figure by Adding
POOL The dimensions of an irregularly shaped
pool are shown. What is the area of the surface
of the pool?
The figure can be separated into a rectangle with
dimensions 16 feet by 32 feet, a triangle with a
base of 32 feet and a height of 15 feet, and two
semicircles with radii of 8 feet.
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Example 4
Find the Area of a Composite Figure by Adding
Area of composite figure
953.1
Answer The area of the composite figure is
953.1 square feet to the nearest tenth.
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Example 4
Find the area of the figure in square feet. Round
to the nearest tenth if necessary.
A. 478.5 ft2 B. 311.2 ft2 C. 351.2 ft2 D. 438.5
ft2

1. A
2. B
3. C
4. D

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Example 5
Find the Area of a Composite Figure by Subtracting
Find the area of the shaded figure.
To find the area of the figure, subtract the area
of the smaller rectangle from the area of the
larger rectangle. The length of the larger
rectangle is 25 100 25 or 150 feet. The width
of the larger rectangle is 25 20 25 or 70
feet.
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Example 5
Find the Area of a Composite Figure by Subtracting
area of shaded figure area
of larger rectangle area of smaller rectangle
Area formulas
Substitution
Simplify.
Simplify.
Answer The area of the shaded figure is 8500
square feet.
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Example 5
INTERIOR DESIGN Cara wants to wallpaper one wall
of her family room. She has a fireplace in the
center of the wall. Find the area of the wall
around the fireplace.
A. 168 ft2 B. 156 ft2 C. 204 ft2 D. 180 ft2

1. A
2. B
3. C
4. D

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End of the Lesson