# Geometry: Perimeter and Area

```Geometry:
Perimeter
and Area
Melissa Kramer
Laingsburg High School
Laingsburg, Michigan
A polygon is a
closed plane
figure formed by
three or more
segments
Each segment intersects
exactly two others at their
endpoints.
Names of Polygons
# of Sides
Name
3
Triangle
4
5
6
7
Heptagon
8
9
10
Nonagon
Names of Polygons
# of Sides
Name
3
Triangle
4
5
Pentagon
6
7
Heptagon
8
9
10
Nonagon
Names of Polygons
# of Sides
Name
3
Triangle
4
5
Pentagon
6
Hexagon
7
Heptagon
8
9
10
Nonagon
Names of Polygons
# of Sides
Name
3
Triangle
4
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Names of Polygons
# of Sides
Name
3
Triangle
4
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
Two Types of Polygons
 Concave:
Has at least one corner
“pushed in” toward the center
 Convex:
center
All corners point away from the
Essential Understanding:
 Perimeter
and area are two DIFFERENT
ways of measuring geometric figures
 The perimeter (notated “P”) of a
polygon is the sum of the lengths of its
sides
 The area (notated “A”) of a polygon is
the number of square units it encloses
 Many figures have formulas to calculate
their perimeter and area.
Which do you need to know: area
or perimeter?
 The
amount of carpet for the basement
floor

Area
 The

Perimeter
 The

amount of fence for a dog run
amount of paint for the bedroom
Area
 The
amount of Halloween lights to hang
around the window

Perimeter
General Formulas
Problem 1
want to frame
a 5 in by 7 in
picture with a 1-inwide frame.
 What is the
perimeter of the
picture?
 What is the
perimeter of the
outside edge of
the frame?
9 in
 You
5 in
7 in
Problem 1
P=2(5 in) + 2(7 in)
P=10 in + 14 in
Perimeter of the
picture is 24 inches
9 in
Perimeter of a
rectangle has a
formula: P=2l + 2w
5 in
7 in
Problem 1
P=2(7 in) + 2(9 in)
P=14 in + 18 in
Perimeter of the
picture is 32 inches
9 in
Perimeter of a
rectangle has a
formula: P=2l + 2w
5 in
7 in
Circles
have special notation
and formulas
is the notation for circle. The
point that represents the center of
the circle is listed to the right of
the notation

 How
 Circle with center W
Circles and Pi
 The
formulas for a circle involve the
special number pi (). Pi is the ratio
of any circle’s circumference
(perimeter) to its diameter. Pi is an
irrational number.
  = 3.1415926…
A
close approximation is
22
7
Problem 2
 What
is the
circumference and
area of the circle
at the right?
Problem 2
 15
inches is the
diameter, so we’ll need
to use the
circumference formula
with “d”
 𝐶 = 𝜋(𝑑)
 𝐶 = 𝜋 15 𝑖𝑛
 𝐶 = 15𝜋 𝑖𝑛

Problem 2
 15
inches is the
diameter, so we’ll need
to use the
circumference formula
with “d”
 𝐶 = 𝜋(𝑑)
 𝐶 = 𝜋 15 𝑖𝑛
 𝐶 = 15𝜋 𝑖𝑛 ≈ 47.1 𝑖𝑛𝑐ℎ𝑒𝑠

approximate
Problem 2
 What
is the
circumference and
area of the circle
at the right?
 The area formula
which is one-half
the diameter
 𝑟 = 7.5 𝑖𝑛
Problem 2
 What
is the
circumference and area
of the circle at the right?
 𝐴 = 𝜋𝑟 2
 𝐴 = 𝜋7.52
 𝐴 ≈ 176.7 𝑖𝑛2

This is the approximate
Finding Area of a Rectangle
 You
are designing
a poster that will
be 3 yd wide and 8
ft high. How much
paper do you
need to make the
poster? Give your
nearest square
foot.
 Your
units must be
the same.
 1 𝑦𝑑 = 3 𝑓𝑡
 3 𝑦𝑑 = 9 𝑓𝑡
Finding Area of a Rectangle
 Use
the area for a
rectangle formula
𝐴 =𝑙 𝑤
 𝐴 = 9 𝑓𝑡 8 𝑓𝑡
 𝐴 = 72 𝑓𝑡 2
 You need 72 𝑓𝑡 2 of
paper to make the
poster
 Your
units must be
the same.
 1 𝑦𝑑 = 3 𝑓𝑡
 3 𝑦𝑑 = 9 𝑓𝑡
 The
units of the
floor plan at the
right are in feet.
Find the perimeter
and area of each
room.
 a. the kitchen
 b. the bedroom
 c. the bathroom
 d. the closet
```
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