Transcript Slide 1

10-1 Area of Rectangles and Parallelograms
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
10-1 Area of Rectangles and Parallelograms
Warm Up
1. What is the perimeter of a square with side
60 in.
lengths of 15 in.?
2. What is the perimeter of a rectangle with
length 16 cm and width 11 cm? 54 cm
10-1 Area of Rectangles and Parallelograms
Problem of the Day
Two wibbles equal four wabbles, and
eight wabbles equal two bibbles. If a
square has a perimeter of 16 wibbles,
what is its area in square bibbles?
4 square bibbles
10-1 Area of Rectangles and Parallelograms
Learn to estimate the area of irregular
figures and to find the area of rectangles
and parallelograms.
10-1 Area of Rectangles and Parallelograms
Vocabulary
area
10-1 Area of Rectangles and Parallelograms
The area of a figure is the amount
of surface it covers. We measure
area in square units.
10-1 Area of Rectangles and Parallelograms
Additional Example 1: Estimating the Area of an
Irregular Figure
Find the area of the rectangle.
Count full squares: 19 red squares.
Count almost-full squares: 9 blue
squares.
Count squares that are about halffull: 4 green squares = 2 full
squares.
Do not count almost empty yellow
squares.
Add. 19 + 9 + 2 = 30
2
The area of the figure is about 30 mi .
10-1 Area of Rectangles and Parallelograms
Check It Out: Example 1
Estimate the are of the figure.
Count full squares: 11 red squares.
Count almost-full squares: 5
green squares.
Count squares that are about halffull: 4 blue squares = 2 full
= mi2
squares.
Do not count almost empty yellow
squares.
Add. 11 + 5 + 2 = 18
The area of the figure is about 18 mi2.
10-1 Area of Rectangles and Parallelograms
10-1 Area of Rectangles and Parallelograms
Additional Example 2: Finding the Area of a
Rectangle
Find the area of the figure.
15 in.
9 in.
A = lw
A = 15
Write the formula.
•
A = 135
9
Substitute 15 for l.
Substitute 9 for w.
The area is about 135 in2.
10-1 Area of Rectangles and Parallelograms
Check It Out: Example 2
Find the area of the figure.
13 in.
7 in.
A = lw
A = 13
A = 91
Write the formula.
•
7
Substitute 13 for l.
Substitute 7 for w.
The area is about 91 in2.
10-1 Area of Rectangles and Parallelograms
You can use the formula for the area of a rectangle
to write a formula for the area of a parallelogram.
Imagine cutting off the triangle drawn in the
parallelogram and sliding it to the right to form a
rectangle.
The area of a parallelogram = bh.
The area of a rectangle = lw.
The base of the parallelogram is the length of the
rectangle. The height of the parallelogram is the
width of the rectangle.
10-1 Area of Rectangles and Parallelograms
Additional Example 3: Finding the Area of a
Parallelogram
Find the area of the parallelogram.
1 1 ft
4
2 1 ft
2
A = bh
Write the formula.
1
__
1
1
__ __ Substitute 2 for b
A=2 •1
2
2
4
1
__
and 1 for h.
4
5
5
__
__
A=
•
Multiply.
2
4
25
1
___
__
A=
or 3
8
8
1 2
__
The area is 3 ft .
8
10-1 Area of Rectangles and Parallelograms
Check It Out: Example 3
Find the area of the parallelogram.
3 1 ft
2
1 1 ft
2
A = bh
Write the formula.
1
1
1
__
__
__
A=1 •3
2
2 Substitute 1 2 for b
1
__
and 3 for h.
2
3
7
A = __ • __
Multiply.
2
2
21
1
A = ___ or 5 __
4
4
1 2
__
The area is 5 4 ft .
10-1 Area of Rectangles and Parallelograms
Additional Example 4: Recreation Application
Jessika is going to tile a kitchen that
measures 13 ft by 17 ft. Some floor space is
taken up by an island that measures 3 ft by 6
ft. How much area remains to be tiled in the
kitchen?
To find the area to be tiled, subtract the area of
the island from the area of the floor.
– island = kitchen area to be tiled
floor area
(13 • 17)
–
(3 • 6)
=
n
221
–
18
=
203
Substitute for l
and w in A = lw.
Use the order of
operations.
The area of the kitchen to be tiled is 203 ft2.
10-1 Area of Rectangles and Parallelograms
Check It Out: Example 4
Miguel is going to landscape his backyard that
measures 16 ft by 11 ft. Some of the backyard
space is taken up by a built-in BBQ that
measures 2 ft by 4 ft. How much area remains
to be landscaped?
To find the landscaped area, subtract the area of
the BBQ from the area of the backyard.
= landscaped area
backyard area –
BBQ
Substitute for l
and w in A = lw.
176
–
8
= 168 Use the order of
operations.
The area of the backyard to be landscaped is 168 ft2.
(16 • 11)
–
(2 • 4)
=
n
10-1 Area of Rectangles and Parallelograms
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
10-1 Area of Rectangles and Parallelograms
Lesson Quiz
Find the area of each figure.
1.
2.
41.4 m2
48 ft2
3. What is the area of a parallelogram with base 16
160 in2
in. and height 10 in.?
4. A square fish pond that is 6 ft long is
surrounded by a square walk that is 18 ft long.
What is the area covered by the walk? 288 ft2
10-1 Area of Rectangles and Parallelograms
Lesson Quiz for Student Response Systems
1. Find the area of the figure.
A. 53.9 m2
B. 53.9 m2
C. 54.6 m2
D. 54.9 m2
10-1 Area of Rectangles and Parallelograms
Lesson Quiz for Student Response Systems
2. Find the area of the figure.
A. 60 ft2
B. 70 ft2
C. 80 ft2
D. 90 ft2
10-1 Area of Rectangles and Parallelograms
Lesson Quiz for Student Response Systems
3. Find the area of a parallelogram with base
19 ft and height 11 ft.
A. 209 ft2
B. 214 ft2
C. 216 ft2
D. 220 ft2