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1.6 – Classify Polygons
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Polygon:
Plane figure that is formed by 3 or more segments, called sides such that:
1. Each side intersects exactly 2 other sides, once at each endpoint
2. No sides with a common endpoint are collinear
3. No curved sides
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Side: Line segment forming the polygon
M
T
SR
Q
QM
MT
TS
SR
RQ
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Vertex: Point where two sides meet
M
T
SR
Q
MTS
R
Q
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Consecutive Sides: Two sides that share a point, one after the other
M
T
SR
Q
and MTQM
and QRQM
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Diagonal: Segment that joins two nonconsecutive sides
M
T
SR
Q
QT
QS
MS
MR
TR
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# of sides Name3456789
101112n
trianglequadrilateral
pentagonhexagonheptagonoctagon
nonagondecagon
? Extra Credit!dodecagon
n-gon
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Convex: No line that contains a side of the polygon contains a point in the interior of the polygon. (rubberband)
Concave: Not convex! Think of a cave going inward!
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State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Curved side
Yes, Concave or ConvexOR
No, _________________
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State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Yes, Concave or ConvexOR
No, _________________
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State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Yes, Concave or ConvexOR
No, _________________
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State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Yes, Concave or ConvexOR
No, ____________________Side touches 3 other sides
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Equilateral Equiangular Regular
All sides are congruent
All angles are congruent
All sides AND all angles are congruent
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
Regular
Hexagon
All sides and angles
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
Regular
quadrilateral
All sides and angles
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
Equiangular
Octagon
All angles , but not all sides
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
equilateral
decagon
All sides , but not all angles
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
Regular
Heptagon
All sides and angles
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Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.
Equilateral
Quadrilateral
All sides , but not all angles
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3. The lengths (in feet) of two sides of a regular quadrilateral are represented by the expressions 8x – 6 and 4x + 22. Find the length of a side of the quadrilateral.
8x – 6
4x + 22
8x – 6 = 4x + 22
4x – 6 = 22
4x = 28x = 7
Side Length = 8(7) – 6 = 50
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1.7 - Find Perimeter, Circumference, and Area
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Area:
Perimeter:
Square units inside a shape.
Measured in u2
cm2, in2, ft2
Length around a shape.
Measured in ucm, in, ft, yd
, yd2
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sP 4 2sA
Square:
s
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wA wP 22
Rectangle:
bhA
w
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cbaP bhA21
Triangle:
b
a ch
b
a ch
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rC 2 2rA
Circle:d
dC
Diameter = 2 radius
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1. Find the perimeter and area of the shaded figure.
sP 4 2sA )8(4P
inP 32
2)8(A264inA
Perimeter: _____________
Area: __________________
inP 32264inA
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1. Find the perimeter and area of the shaded figure.
298 ftA
Perimeter: _____________
Area: __________________
wP 22 bhA )7(2)14(2 P
1428PftP 42
)7)(14(A
ftP 42298 ftA
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1. Find the perimeter and area of the shaded figure.
cbaP bhA21
343016 PinP 80 )16)(30(
21
A
)16(15A2240inA
Perimeter: _____________
Area: __________________
inP 802240inA
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1. Find the perimeter and area of the shaded figure.
cbaP bhA21
204839 PcmP 107 )15)(48(
21
A
A 24(15)
A 360cm2
Perimeter: _____________
Area: __________________
cmP 107
A 360cm2
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2. Find the perimeter and area of the shaded figure.
Perimeter: _____________
Area: __________________
2rA dC )49(C
cmC 49 224.5A
A 600.25cm2
A 600.25cm2
cmC 49
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1. Find the perimeter and area of the shaded figure.
cbaP bhA21
13107 PmP 30 )5)(10(
21
A
)5(5A225mA
Perimeter: _____________
Area: __________________
mP 30225mA
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4. Use the information about the figure to find the indicated measure.
Perimeter = 84ftFind the length. wP 22
)13(2284 26284
258 ft29
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Area = 432m2
Find the width.
4. Use the information about the figure to find the indicated measure.
2A s2432 s
432 s
s 2 2 3 3 s 12 3m
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Area = 189cm2
Find the height.
4. Use the information about the figure to find the indicated measure.
bhA21
h)21(21189
189 10.5h
hcm 18
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HW Problem
# 40a (hexagon)
1.6
1.7
44-47
52-56
1-13 odd, 14, 15-27 odd, 37, 40(a only), 41
1-15 odd, 27-29, 34-37, 41
Ans: 6 sides, 9 diagonals
**Bring ALL supplies tomorrow for review