Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
11­4 Areas of Regular Polygons and Composite Figures
Learning Targets:
I can find areas of regular polygons
I can find areas of composite figures
How many sides does the table have?
If the area of one of the triangular sections of the table is 5 square feet, what is the area of the table?
How can you find the area of a table that is composed of 10 triangular parts?
Apr 1­5:27 PM
Apr 27­1:30 PM
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
When a regular polygon is inscribed in a circle, the center and the radius of the circle are also the center and the radius of the polygon.
Apothem: a segment from the center of a regular polygon perpendicular to a side of the polygon.
Central angle of a regular polygon: its vertex is at the center of the polygon and its sides pass through consecutive vertices of the polygon.
Apr 1­5:32 PM
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Example 1:
1. In the figure, pentagon PQRST is inscribed in X. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle.
2. In the figure, regular hexagon JKLMNP is inscribed in R. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle.
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Example 2:
3. 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?
4. The cover of the hot tub shown is a regular pentagon. If the side length is 2.5 feet and the apothem is 1.7 feet, find the area of the lid to the nearest tenth.
Apr 1­5:43 PM
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Apr 1­5:48 PM
Example 3: Find the area of each regular polygon. Round to the nearest tenth.
5. regular hexagon
6. regular pentagon
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Find the area of each regular polygon. Round to the nearest tenth.
8. 9.
10.
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Composite figure: a figure that can be separated into regions that are basic figures, such as triangles, rectangles, trapezoids, and circles. Apr 2­6:29 AM
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Example 4: 11. The dimensions of an irregularly shaped pool are shown. What is the area of the surface of the pool?
Find the area of each figure. Round to the nearest tenth if necessary.
12. 13.
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Geo 11­4 Lesson with notes 4th b.notebook
April 27, 2016
Example 5: Find the area of the shaded figure.
14. 15.
16.
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