Download Polygons and Perimeter Polygon

10.3
Polygons, Perimeters, and Tessellations
HW: (1-37 Odds, 47, 49)
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Objectives
1. Name certain polygons according to the number of
sides.
2. Recognize the characteristics of certain
quadrilaterals.
3. Solve problems involving a polygon’s perimeter.
4. Find the sum of the measures of a polygon’s angles.
5. Understand tessellations and their angle
requirements.
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Polygons and Perimeter
• Polygon: Any ___________ _________ in the plane
formed by three or more line segments that intersect
only at their endpoints.
• Regular Polygon: Has sides which are all the same
__________ and angles of all the same ___________.
• Perimeter of a Polygon: The _______ of the
__________ of its sides.
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Regular Polygons
Name
Triangle
3 sides
Quadrilateral
4 sides
Pentagon
5 sides
Picture
Name
Hexagon
6 sides
Picture
Heptagon
7 sides
Octagon
8 sides
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Types of Quadrilaterals
Name
Characteristics
Parallelogram
Quadrilateral in which both pairs of opposite
_________ are parallel and have the same
measure. Opposite ____________ have the
same measure
Rhombus
Parallelogram with all sides having equal
____________.
Rectangle
Parallelogram with four ________ angles.
Because a rectangle is a parallelogram,
opposite sides are __________________ and
have the same measure.
Square
A rectangle with all sides having equal
__________. Each angle measures _____,
and the square is a regular quadrilateral.
Trapezoid
A quadrilateral with exactly ______ pair of
parallel sides.
Representation
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Example 1: An Application of Perimeter
Fencing costs $5.25 per foot.
Find the cost to enclose the field
with fencing.
a. Find the perimeter.
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Example 1 continued
Fencing costs $5.25 per foot.
Find the cost to enclose the field
with fencing.
b. Convert to feet.
c. Multiply by the cost per foot.
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Example 2: The Sum of the Measures of a
Polygon’s Angles
The sum of the measures of the angles of a polygon
with n sides is (n – 2)180º.
Find the sum of the measures of the angles of an
octagon.
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Tessellations (Tiling)
• A pattern consisting of the ________________ use of
the same geometric figures to completely cover a
plane, leaving no _________ and no overlaps.
• The sum of the measures of the angles that come
together at each __________ is always _______º.
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Examples of Tessellations
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Example 3: Angle Requirements of
Tessellations
Explain why a tessellation cannot be
created using only regular pentagons.
Solution: Apply (n − 2)180º to find
the measure of each angle of a regular pentagon.
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