Geometry
1.4 Perimeter and Area in the
Coordinate Plane
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
1.4 Warm Up
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Essential Question
How can you find the perimeter and area
of a quadrilateral in a coordinate plane?
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
What You Will Learn
• Classify polygons
• Find perimeters and areas of polygons in the
coordinate plane.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Polygons
• A plane figure made of three or more segments
(sides).
• Each side intersects exactly two other sides at their
endpoints.
• Polygons are named by vertices in consecutive
order, going CW or CCW.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
These are Polygons
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
These are NOT polygons.
No
Segments/sides
1.4 Perimeter and Area in the Coordinate Plane
Sides don’t
intersect at
endpoints.
Figure not
closed.
August 25, 2016
Naming Polygons
• The name tells you how many sides and how many
vertices the polygon has.
• Learn the names: memorize!
• Be able to spell them.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Triangle – 3 sides
C
We say “Triangle ABC”
A
1.4 Perimeter and Area in the Coordinate Plane
B
Vertex B
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Quadrilateral – 4 sides
Q
T
Name: QRST
R
1.4 Perimeter and Area in the Coordinate Plane
S
We say “Quadrilateral QRST”
August 25, 2016
Pentagon – 5 sides
N
Name: JKLMN
J
1.4 Perimeter and Area in the Coordinate Plane
M
K
L
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Hexagon – 6 sides
C
B
Name: FEDCBA
A
D
1.4 Perimeter and Area in the Coordinate Plane
E
F
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Heptagon – 7 sides
1.4 Perimeter and Area in the Coordinate Plane
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Octagon – 8 sides
1.4 Perimeter and Area in the Coordinate Plane
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Nonagon – 9 sides
1.4 Perimeter and Area in the Coordinate Plane
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Decagon – 10 sides
1.4 Perimeter and Area in the Coordinate Plane
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Names used on occasion
• undecagon – 11 sides (1 + 10 sides)
• dodecagon – 12 sides (2 + 10 sides)
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
More than 10 sides: n-gon
• 14-gon has 14 sides.
• 200-gon has 200 sides.
• 36-gon has 36 sides.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Convex & Concave
• All polygons are either convex or concave.
• It’s easy to determine which category falls in just
by looking.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Convex
• No extended sides are in the interior of the polygon.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Think: Caved In
Concave
• At least one extended side (or part of one) is in the
interior of the polygon.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Example 1
Classify each polygon by the number of sides. Tell
whether it is convex of concave.
a.
b.
Hexagon,
Convex
Quadrilateral,
Concave
c.
d.
Heptagon,
Convex
1.4 Perimeter and Area in the Coordinate Plane
Pentagon,
Concave
August 25, 2016
Perimeter and Area
Perimeter – The distance around a
figure.
Area – The square units it takes to
fill a figure.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Square
Perimeter
S
P = 4s
S
Area
A = s2
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Rectangle
Perimeter
h
b
1.4 Perimeter and Area in the Coordinate Plane
P = 2b + 2h
Area
A = bh
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Parallelogram
Perimeter
h
b
1.4 Perimeter and Area in the Coordinate Plane
P = add all sides
Area
A = bh
August 25, 2016
Triangle
Perimeter
a
c
h
P = add all sides
Area
A  bh
1
2
b
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Example 2
Each side of a square measures 2.5 m. Find its
perimeter and its area.
P = 4(2.5) = 10 m
2.5 m
A = 2.52 = 6.25 m2
2.5 m
1.4 Perimeter and Area in the Coordinate Plane
Area is a
square
measure.
August 25, 2016
Example 3
Find the perimeter and the area.
8 in
3 in
2 in
10 in
P = 3 + 10 + 8 = 21 in
A = ½ (10)(2) = 10 in2
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Example 4
a. Find the perimeter of GRAM with vertices G(0, 1),
R(-2, -3), A(3, -3), and M(5, 1).
G(0, 1)
R(-2, -3)
M(5, 1)
A(3,-3)
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Example 4
b. Find the area of GRAM with vertices G(0, 1),
R(-2, -3), A(3, -3), and M(5, 1).
G(0, 1)
R(-2, -3)
M(5, 1)
A(3,-3)
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Example 5
You are building a shed in your backyard. The diagram shows the
four vertices of the shed. Each unit in the coordinate plane
represents 1 foot. Find the area of the floor of the shed.
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Essential Question
How can you find the perimeter and area
of a quadrilateral in a coordinate plane?
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016
Assignment
1.4 worksheet
1.4 Perimeter and Area in the Coordinate Plane
August 25, 2016