Geometry
1.4 Perimeter and Area in the
Coordinate Plane
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Essential Question
How can I find the perimeter and area of
a polygon in a coordinate plane?
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
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
September 1, 2015
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
September 1, 2015
Examples
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
These are NOT polygons.
No Sides or
Segments
1.4 Perimeter and Area in the Coordinate Plane
Sides don’t
intersect at
endpoints.
Figure not
closed.
September 1, 2015
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
September 1, 2015
Triangle – 3 sides
C
We say “Triangle ABC”
A
1.4 Perimeter and Area in the Coordinate Plane
B
Vertex B
September 1, 2015
Quadrilateral – 4 sides
Q
T
Name: QRST
We say “Quadrilateral QRST”
R
1.4 Perimeter and Area in the Coordinate Plane
S
September 1, 2015
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
September 1, 2015
Octagon – 8 sides
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Nonagon – 9 sides
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Decagon – 10 sides
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
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
September 1, 2015
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
September 1, 2015
Convex
• No extended sides are in the interior of the polygon.
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
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
September 1, 2015
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
September 1, 2015
Triangle
Perimeter
a
c
h
P=a+b+c
Area
A  bh
1
2
b
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Square
Perimeter
S
P = 4s
S
Area
A = s2
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Rectangle
Perimeter
P
=
2
l
+
2w
w
l
1.4 Perimeter and Area in the Coordinate Plane
Area
A = lw
September 1, 2015
Example 2
Each side of a square measures 2.5 m. Find its
perimeter and its area.
P = 4(2.5) = 10 m
A = 2.52 = 6.25 m2
2.5 m
2.5 m
1.4 Perimeter and Area in the Coordinate Plane
Area is a
square
measure.
September 1, 2015
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
September 1, 2015
Example 4
C(-2, 3)
A(3,-3)
T(-2, -3)
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Example 5
D(1, 3)
O(4,-3)
G(-4, -3)
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Example 6
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
September 1, 2015
Essential Question
How can you find the perimeter and area
of a polygon in a coordinate plane?
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015
Assignment
In the Student Math Jounals
(the soft cover one)
Do all the problems on page 20. 
1.4 Perimeter and Area in the Coordinate Plane
September 1, 2015