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Geometry
1.7 Introduction to Perimeter,
Circumference, and Area
Perimeter vs Area
• Perimeter is the distance around the shape
• Area is the amount of space the shape takes
up….what is inside
SQUARE
Side length s
• Perimeter (P)
P = 4s
• Area (A)
A = s2
RECTANGLE
Length l and width w
• Perimeter (P)
P = 2l + 2w
• Area (A)
A=lw
TRIANGLE
side lengths a, b, and c,
base b, and height h
• Perimeter (P)
P=a+b+c
• Area (A)
A = (1/2)bh
CIRCLE
Radius r
• Circumference (C)
C = 2πr
• Area (A)
A = πr²
Example 1
Find the perimeter and area of a rectangle of
length 4.5m and width 0.5m
0.5
4.5
Solution
Area
Perimeter
A=lw
P = 2l + 2w
A = (4.5)(.5)
P = 2(4.5) + 2(.5)
A = 2.25 m2
P=9+1
P = 10 m
Example 2
A road sign consists of a
pole with a circular sign
on top. The top of the
circle is 10 feet high and
the bottom of the circle
is 6 feet high. Find the
diameter, radius,
circumference, and area
of the circle. Use 3.14 as
an approximation for π.
Example 3
Find the area and perimeter of the triangle
defined by H(-2, 3), J(3, -1), K(-2, -4).
Example 4
Find the area and perimeter of the triangle
defined by T(-2, 6), U(4, 6), and V(4, -2).
PROBLEM SOLVING PLAN
1. Ask yourself what you need to solve the problem.
Write a verbal model or draw a sketch that will help
you find what you need to know.
2. Label known and unknown facts on or near your
sketch.
3. Use labels and facts to choose related definitions,
theorems, formulas, or other results you may need.
4. Reason logically to link the facts, using a proof or
other written argument.
5. Write a conclusion that answers the original problem.
Check that your reasoning is correct.
Example 5
A maintenance worker needs to fertilize a 9hole golf course. The entire golf course covers
a rectangular area that is approximately 1800
feet by 2700 feet. Each bag of fertilizer covers
20,000 square feet. How many bags will the
worker need?
Example 6
You are designing a mat for a picture. The
picture is 8 inches wide and 10 inches tall.
The mat is to be 2 inches wide. What is the
area of the mat?
Example 7
You are making a triangular window. The
height of the window is 18 inches and the
area should be 297 inches. What should the
base of the window be.
Example 8
A painter is painting one side of a wooden
fence along a highway. The fence is 926 feet
long and 12 feet tall. The directions on each 5
gallon paint can say that each can will cover
2000 square feet. How many cans of paint will
be needed to paint the fence?
Example 9
You are planning a deck along two sides of a
pool. The pool measures 18 feet by 12 feet.
The deck is to be 8 feet wide. What is the
area of the deck?
Example 10
You are making a triangular flag with a base of
24 inches and an area of 360 square inches.
How long should it be.