Transcript Break Into Simpler Parts

10-3 Break into Simpler Parts
Warm Up
Problem of the Day
Lesson Presentation
Course 1
10-3 Break into Simpler Parts
Warm Up
1. What is the area of a rectangle with
length 10 cm and width 4 cm? 40 cm2
2. What is the area of a parallelogram with
base 18 ft and height 12 ft? 216 ft2
3. What is the area of a triangle with base
16 cm and height 8 cm? 64 cm2
Course 1
10-3 Break into Simpler Parts
Problem of the Day
Four squares are stacked in a tower.
The bottom square is 12 inches on a
side. The perimeter of each of the other
squares is half of the one below it. What
is the perimeter of the combined figure?
69 in.
Course 1
10-3 Break into Simpler Parts
Learn to break a polygon into simpler
parts to find its area.
Course 1
10-3 Break into Simpler Parts
Additional Example 1A: Finding Areas of
Composite Figures
Find the area of the polygon.
1.7 cm
A.
1.3 cm
4.9 cm
2.1 cm
Think: Break the polygon apart into
rectangles.
Find the area of each rectangle.
Course 1
10-3 Break into Simpler Parts
Additional Example 1A Continued
1.7 cm
1.3 cm
4.9 cm
2.1 cm
A = lw
A = lw
A = 4.9 • 1.7
A = 8.33
A = 2.1
•
A = 2.73
Write the formula
1.3 for the area of a
rectangle.
8.33 + 2.73 = 11.06
Add to find the total area.
The area of the polygon is 11.06 cm2.
Course 1
10-3 Break into Simpler Parts
Additional Example 1B Continued
Find the area of the polygon.
B.
Think: Break the figure apart into a
rectangle and a triangle.
Find the area of each polygon.
Course 1
10-3 Break into Simpler Parts
Additional Example 1B Continued
A = lw
A = 28 • 24
A = 672
1
__
A = bh
2
1
__
A = 28 • 12
2
A = 168
Add to find the total area
of the polygon.
The area of the polygon is 840 ft2.
672 + 168 = 840
Course 1
10-3 Break into Simpler Parts
Try This: Example 1A
Find the area of the polygon.
A.
1.9 cm
5.5 cm
1.9 cm
1.5 cm
5.5 cm
2 cm
3.4 cm
Think: Break the polygon apart into
rectangles.
Find the area of each rectangle.
Course 1
1.5 cm
2 cm
10-3 Break into Simpler Parts
Try This: Example 1A Continued
1.9 cm
5.5 cm
1.5 cm
2 cm
A = lw
A = lw
A = 5.5 • 1.9
A = 10.45
A=2
A=3
•
1.5
Write the formula
for the area of a
rectangle.
10.45 + 3 = 13.45
Add to find the total area.
The area of the polygon is 13.45 cm2.
Course 1
10-3 Break into Simpler Parts
Try This: Example 1B
Find the area of the polygon.
16 ft
22 ft
B.
20 ft
36 ft
22 ft
20 ft
22 ft
Think: Break the figure apart into a
rectangle and a triangle.
Find the area of each polygon.
Course 1
10-3 Break into Simpler Parts
Try This: Example 1B Continued
16 ft
22 ft
20 ft
22 ft
A = lw
A = 22 • 20
A = 440
1
__
A = bh
2
1
__
A = 22 • 16
2
A = 176
Add to find the total area
of the polygon.
The area of the polygon is 616 ft2.
440 + 176 = 616
Course 1
10-3 Break into Simpler Parts
Additional Example 2: Art Application
Patrick made a design. All the sides are 5 inches
long, except for two longer sides that are each 20
inches. All the angles are right angles. What is the
area of the quilt design?
20 in.
Think: Divide the design into 3
rectangles. Find the area of one
rectangle that has a length of 20 in
5 in.
20 in.
and a width of 5 in.
A = lw
Write the formula.
A = 20 • 5 = 100
Multiply to find the area of the 3
3 • 100 = 300
rectangles.
The area of the design is 300 in2.
Course 1
10-3 Break into Simpler Parts
Helpful Hint
You can also use the formula A = s2 , where s is
the length of a side, to find the area of a square.
Course 1
10-3 Break into Simpler Parts
Try This: Example 2
Yvonne made quilt design. All the sides are 4 inches
long, except for the two longer sides that are each
16 inches. All the angles are right angles. What is
the area of the quilt design?
4 in.
16 in.
A = lw
Think: Divide the quilt design into
16 in. 10 squares. Find the area of one
square that has a side length of 4 in.
A = 4 • 4 = 16
Write the formula.
Multiply to find the area of the
10 • 16 = 160
10 squares.
The area of the quilt design is 160 in2.
Course 1
10-3 Break
Insert into
Lesson
Simpler
TitleParts
Here
Lesson Quiz
Find the area of the figure shown.
220 units2
Course 1