The document discusses perimeter, circumference, and area. It defines that perimeter and circumference are measured in units of length, while area is measured in square units. It also provides formulas for calculating the circumference and area of circles using pi. Examples are given for calculating perimeter, circumference, and area of rectangles and circles.

1. 1.7 Notes
Perimeter, Circumference, Area.

2. 1.7 Notes
Perimeter, Circumference, Area.
Perimeter & circumference are measured in units of length
(inches, feet, yards, miles, meters, kilometers, centimeters, etc).

Area is measured in “square units,” using the following
notation: “square feet” – ft2, “square inches” – in2,
“square meters” m2, etc.†



In a circle, the radius is ½ of the diameter, and the diameter is
2 times as long as the radius (r = d/2 or d =2r)
For π, use either 3.14 or the button on the calculator
(3.141592654…)
†Ask Dr. Math for a discussion on “square units” vs. “units squared.”

3. EXAMPLE 1
Find the perimeter and area of a rectangle
Basketball
Find the perimeter and area of the
rectangular basketball court shown.
SOLUTION
Perimeter
P = 2l + 2w
= 2(84) + 2(50)
= 268
ANSWER
Area
A = lw
= 84(50)
= 4200
The perimeter is 268 feet and the area is
4200 square feet.

4. EXAMPLE 2
Find the circumference and area of a circle
Team Patch
You are ordering circular cloth
patches for your soccer team’s
uniforms. Find the approximate
circumference and area of the
patch shown.
SOLUTION
First find the radius. The diameter is 9 centimeters, so
the radius is 1 (9) = 4.5 centimeters.
2
Then find the circumference and area.
Use 3.14 to approximate the value of π.

5. EXAMPLE 2
Find the circumference and area of a circle
C = 2πr
2(3.14) (4.5)
= 28.26
A = πr 2
3.14(4.5)
= 63.585
ANSWER
The circumference is about 28.3 cm2.
The area is about 63.6 cm .
2

6. GUIDED PRACTICE
for Examples 1 and 2
Find the area and perimeter (or circumference) of the
figure. If necessary, round to the nearest tenth.
ANSWER 74.1 m2, 37.4 m

7. GUIDED PRACTICE
for Examples 1 and 2
Find the area and perimeter (or circumference) of the
figure. If necessary, round to the nearest tenth.
ANSWER 2.6 cm2, 6.4 cm

8. GUIDED PRACTICE
for Examples 1 and 2
Find the area and perimeter (or circumference) of the
figure. If necessary, round to the nearest tenth.
ANSWER 12.6 yd2, 12.6 yd

9. EXAMPLE 3
Perimeter & Area in the coordinate plane
What is the perimeter of triangle
RQS? What is the area?
Animated
Solution
Answers: perimeter
13.1 units; area = 8 square units.

10. EXAMPLE 4
Solve a multi-step problem
Skating Rink
An ice-resurfacing machine is
used to smooth the surface of the
ice at a skating rink. The machine
can resurface about 270 square
yards of ice in one minute.
About how many minutes does it take the machine to
resurface a rectangular skating rink that is 200 feet
long and 90 feet wide?
SOLUTION
The machine can resurface the ice at a rate of 270
square yards per minute. So, the amount of time it takes
to resurface the skating rink depends on its area.

11. EXAMPLE 4
STEP 1
Solve a multi-step problem
Find the area of the rectangular skating rink.
Area = lw = 200 (90) = 18,000 ft 2
The resurfacing rate is in square yards per
minute. Rewrite the area of the rink in square
yards. There are 3 feet in 1 yard, and 32 = 9
square feet in 1 square yard.
18,000 ft
2
1 yd 2 2000 yd 2
=
9 ft 2
Use unit analysis.

12. EXAMPLE 4
STEP 2
Solve a multi-step problem
Write a verbal model to represent the
situation. Then write and solve an equation
based on the verbal model.
Let t represent the total time (in minutes)
needed to resurface the skating rink.
2000 = 270 t
7.4
t
ANSWER
Substitute.
Divide each side by 270.
It takes the ice-resurfacing machine about
7 minutes to resurface the skating rink.

13. GUIDED PRACTICE
4.
for Examples 3 and 4
Describe how to find the height from F to EG
in the triangle.
ANSWER
The height is the length of the segment from
point F to EG at the point (1,3). Using the
coordinate grid to count units , the height is 6.

14. GUIDED PRACTICE
for Examples 3 and 4
5. Find the perimeter and the area of the triangle
shown.
ANSWER
about 16.8, 12

15. GUIDED PRACTICE
6.
for Examples 3 and 4
What if ? In Example 4, suppose the skating
rink is twice as long and twice as wide. Will it
take an ice-resurfacing machine twice as long
to resurface the skating rink? Explain your
reasoning.
ANSWER
No; the new area is more than twice as
big.

16. EXAMPLE 5
Find unknown length
The base of a triangle is 28 meters. Its area
is 308 square meters. Find the height of the
triangle.
SOLUTION
1 bh
= 2
308 = 1 (28) h
2
A
22
= h
ANSWER
Write formula for the area of a triangle.
Substitute 308 for A and 28 for b.
Solve for h.
The height is 22 meters.

17. GUIDED PRACTICE
for Example 5
7. The area of a triangle is 64 square meters, and its
height is 16 meters. Find the length of its base.
ANSWER
8 m.

18. EXAMPLE 3
Animated Solution!! Click for steps!!
Perimeter: Use the ruler postulate to
find the length of QS (since it is a
horizontal segment). For RS and RQ,
use the distance formula. Then add up
all the side lengths to find the perimeter.
QS = 5 – 1 = 4 units
QR =
(4 – 1)2+ (6 – 2)2
=
25 = 5 units
RS =
(5 – 4)2+ (2 – 6)2
=
17
4.1 units
Then find the perimeter.
P = QS + QR + RS
4 + 5 + 4.1 = 13.1 units

19. EXAMPLE 3
Animated Solution!! Click for steps!!
Area: You know QS from the previous
problem. To find the height, drop down
from R to segment QS, and use the ruler
postulate again.
QS = 5 – 1 = 4 units
(4, 2)
h = 6 – 2 = 4 units
Then find the area.
A = 1/2 bh
Back to
Notes
A = 1/2 (4)(4)
A=8
The area is 8 square units.