Transcript 1.7 Introduction to Perimeter, Circumference, and Area

Introduction to Perimeter,
Circumference, and Area
1.7
What you should learn
GOAL
1
Find the perimeter and area of common
plane figures.
GOAL
2
Use a general problem-solving plan.
Why you should learn it
To solve real-life problems about perimeter and area,
such as finding the number of bags of seed you need
for a field.
Introduction to Perimeter,
Circumference, and Area
1.7
GOAL
1
REVIEWING PERIMETER,
CIRCUMFERENCE, AND AREA
You are expected to know and be able to use the formulas
for perimeter (P), area (A), and circumference (C) found on
page 51 of the text.
You should have these formulas memorized by the time
you have completed the assignment. They are reviewed
on the next slide.
PERIMETER, CIRCUMFERENCE, AND AREA FORMULAS
s
SQUARE
side length s
s
s
P = 4s
A=
s
s
s2
length l and
width w
P = 2l + 2w
A = lw
TRIANGLE
CIRCLE
side lengths a, b,
and c, base b,
and height h
radius r
P=a+b+c
1
A  bh
2
a
w
RECTANGLE
hcc
a
b
b
C  2 r
A  r 2
l
l
l
w
w
r
You are expected to use the correct type of units for
perimeter, circumference, and area.
The units used for perimeter and circumference are units of
______,
length and the units used for area are ______
square units.
The expression cm2 is read as “square centimeters”, m2 is
read “square meters”, and so on.
Know how to read these and other units correctly!
EXAMPLE 1
Extra Example 1
Find the perimeter and area of a rectangle of length 4.5 m
and width 0.5 m. Hint: draw and label a sketch, then write
the correct formulas.
w = 0.5 m
l = 4.5 m
Click for the solutions
EXAMPLE 2
P  2l  2w
 2(4.5 m)  2(0.5 m)
 10 m
A  lw
  4.5 m 0.5 m
 2.25 m2
Extra 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
8 feet high. Find the diameter, radius, circumference, and
area of the circle. Use 3.14 as an approximation for π, and
round your answers to the nearest tenth.
10 ft
8 ft
diameter
d  10 ft  8 ft
 2 ft
radius
1
r d
2
1
 (2 ft)
2
 1 ft
circumference
C  2 r
 2 1 ft 
 6.3 ft
area
A  r 2
  (1 ft)2
 3.1 ft 2
EXAMPLE 3
Extra Example 3
Find the area and perimeter of the triangle defined by
H(2,2), J (3, 1), and K ( 2, 4). Click to see the triangle.
y
Click to see the solutions.
H(2,2)
L(-2,-1)
K (2, 4)
Area
1
x
A  bh
2
J (3, 1)
1
 (HK )(LJ )
2
1
 (6)(5)
2
 15 units2
Perimeter
P  HK  KJ  JH
(Use the Distance
Formula to find KJ
and JH.)
P  6  2 34 units
Checkpoint
1. A circular compact disc fits exactly in a square box with
sides 12 cm long. Find the diameter, radius, circumference,
and area of the CD, and the perimeter and area of the box.
Use 3.14 as an approximation for π. Click for the answers.
CD: d = 12 cm; r = 6 cm; C ≈ 37.7 cm; A ≈ 113 cm2
Box: P = 48 cm; A = 144 cm
2. Find the area and perimeter of the triangle defined by
Click for the answers.
T (2,6),U(4,6), and V (4, 2).
A = 24 sq. units; P = 24 units
1.6 Angle Pair Relationships
GOAL
2
USING A PROBLEM-SOLVING PLAN
THINK AND DISCUSS:
Why do you need a problem-solving plan?
Our text provides a 5-step plan as shown on the following
slide. You will notice similarities and differences with other
plans, and are expected to speak intelligently about these
steps as well as use them in your work.
A FIVE-STEP PROBLEM-SOLVING PLAN
1. Write a verbal model or draw a sketch.
2. Label your known and unknown facts.
3. Choose definitions, theorems, formulas, or
intermediate results you will need to solve the problem.
4. Reason logically to link the information. Use a proof,
algebraic equations, or other written argument.
5. Write a conclusion that answers the original problem and
check your result.
EXAMPLE 4
Extra Example 4
A maintenance worker needs to fertilize a 9-hole 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?
2700 ft
A = bh
1800 ft
Area of
=
field
(2700 ft)(1800 ft) =
(2700 ft)(1800 ft) = b
20,000 ft2/bag
243 bags = b
# of
bags
b
•
Coverage
per bag
• 20000 ft2/bag
Checkpoint
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 bucket say that each
bucket will cover 2000 square feet. How may buckets of
paint will be needed to paint the fence?
Click for the answer.
He will need 6 buckets.
EXAMPLE 5
Extra Example 5
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? Click for help.
2 in.
10 in.
2 in.
2 8 in.
in.
2
in.
Area
of mat
A
=
Total
area
-
Area of
picture
=
btht
-
bphp
A  (12 in.)(14 in.)  (8 in.)(10 in.)
 88 in.2
EXAMPLE 6
Extra Example 6
You are making a triangular window. The height of the
window is 18 inches and the area should be 297 square
inches. How long should the base of the window be?
Click for the solution.
18 in.
base
Area of
1
Base of
window = 2 • window •
297
in.2
1
= b(18 in.)
2
33 in. = b
Height of
window
Checkpoint
You are designing a quilt that is made of rectangles sewn
together. Each rectangle follows the pattern below. Each of
the small triangles has a base of 3 cm and an area of 9 cm2.
1. What is the height of each of the
small triangles?
h = 6 cm
3 cm
2. What is the area of the border if
its width is 3 cm?
A = 144 cm2
3 cm
Click for the answers.
QUESTIONS?