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Geometry Notes
Perimeter and Area
Page 1 of 57
PERIMETER AND AREA
Objectives:
After completing this section, you should be able to do the following:
• Calculate the area of given geometric figures.
• Calculate the perimeter of given geometric figures.
• Use the Pythagorean Theorem to find the lengths of a side of a right
triangle.
• Solve word problems involving perimeter, area, and/or right triangles.
Vocabulary:
As you read, you should be looking for the following vocabulary words and
their definitions:
• polygon
• perimeter
• area
• trapezoid
• parallelogram
• triangle
• rectangle
• circle
• circumference
• radius
• diameter
• legs (of a right triangle)
• hypotenuse
Formulas:
You should be looking for the following formulas as you read:
• area of a rectangle
• area of a parallelogram
• area of a trapezoid
• area of a triangle
• Heron’s Formula (for area of a triangle)
• circumference of a circle
• area of a circle
• Pythagorean Theorem

Geometry Notes
Perimeter and Area
Page 2 of 57
We are going to start our study of geometry with two-dimensional figures.
We will look at the one-dimensional distance around the figure and the twodimensional space covered by the figure.
perimeter
The perimeter of a shape is defined as the distance around the shape. Since
we usually discuss the perimeter of polygons (closed plane figures whose
sides are straight line segment), we are able to calculate perimeter by just
adding up the lengths of each of the sides. When we talk about the
perimeter of a circle, we call it by the special name of circumference. Since circumference
we don’t have straight sides to add up for the circumference (perimeter) of
a circle, we have a formula for calculating this.
Circumference (Perimeter) of a Circle
C = 2π r
r = radius of the circle
π = the number that is approximated by 3.141593
Example 1:
Find the perimeter of the figure below
14
4
11
8
Solution:
It is tempting to just start adding of the numbers given together,
but that will not give us the perimeter. The reason that it will not
is that this figure has SIX sides and we are only given four
numbers. We must first determine the lengths of the two sides
that are not labeled before we can find the perimeter. Let’s look
at the figure again to find the lengths of the other sides.

Geometry Notes
Perimeter and Area
Page 3 of 57
Since our figure has all right angles, we are able to determine the
length of the sides whose length is not currently printed. Let’s
start with the vertical sides. Looking at the image below, we can
see that the length indicated by the red bracket is the same as
the length of the vertical side whose length is 4 units. This means
that we can calculate the length of the green segment by
subtracting 4 from 11. This means that the green segment is 7
units.
14
4
4
11
11 ― 4 = 7
8
In a similar manner, we can calculate the length of the other
missing side using 14 − 8 = 6 . This gives us the lengths of all the
sides as shown in the figure below.
14
4
11
6
7
8
Now that we have all the lengths of the sides, we can simply
calculate the perimeter by adding the lengths together to get
4 + 14 + 11 + 8 + 7 + 6 = 50. Since perimeters are just the lengths
of lines, the perimeter would be 50 units.
area

Geometry Notes
Perimeter and Area
Page 4 of 57
The area of a shape is defined as the number of square units that cover a
closed figure. For most of the shape that we will be dealing with there is a
formula for calculating the area. In some cases, our shapes will be made up
of more than a single shape. In calculating the area of such shapes, we can
just add the area of each of the single shapes together.
We will start with the formula for the area of a rectangle. Recall that a
rectangle is a quadrilateral with opposite sides parallel and right interior
angles.
Area of a Rectangle
A = bh
b = the base of the rectangle
h = the height of the rectangle
Example 2:
Find the area of the figure below
14
4
11
8
Solution:
This figure is not a single rectangle. It can, however, be broken up
into two rectangles. We then will need to find the area of each of the
rectangles and add them together to calculate the area of the whole
figure.
There is more than one way to break this figure into rectangles. We
will only illustrate one below.
rectangle

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