1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Graph the line segment for each set of ordered pairs. Then find the length of the line segment.
1. (–7, 0), (0, 0)
2. (0, 3), (0, 6)
3. (–4, –2), (1, –2)
4. (–5, 4), (–5, –2)
7 units
3 units
5 units
6 units

3. Problem of the Day
Six pennies are placed around a seventh so that there are no gaps. What figure is formed by connecting the centers of the six outer pennies?
regular hexagon

4. Learn to find the perimeter and area of rectangles and parallelograms.

5. Vocabulary
perimeter
area

6. Any side of a rectangle or parallelogram can be chosen as the base
Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base.
Rectangle
Parallelogram
Height
Height
Side
Base
Base
Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.

7. Additional Example 1A: Finding the Perimeter of Rectangles and Parallelograms
Find the perimeter of the figure. 5 14
P =
Add all side lengths.
= 38 units
or P = 2b + 2h
Perimeter of rectangle.
Substitute 14 for b and 5 for h.
= 2(14) + 2(5)
= = 38 units

8. When referring to the measurements of a rectangle, the terms length (l) and width (w) are sometimes used in place of base (b) and height (h). So the formula for the perimeter of a rectangle can be written as
P = 2b + 2h = 2l + 2w = 2(l + w).
Caution!

9. Additional Example 1B: Finding the Perimeter of Rectangles and Parallelograms
Find the perimeter of the figure. 20 16
P =
Add all side lengths.
= 72 units

10. Check It Out: Example 1A
Find the perimeter of the figure. 6 11
P =
Add all side lengths.
= 34 units
or P = 2b + 2h
Perimeter of rectangle.
Substitute 11 for b and 6 for h.
= 2(11) + 2(6)
= = 34 units

11. Check It Out: Example 1B
Find the perimeter of the figure. 5 13
P =
Add all side lengths.
= 36 units

12. Area is the number of square units in a figure
Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.

13. The formula for the area of a rectangle can also be written as A = lw.
Helpful Hint

14. Additional Example 2A: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
(–1, –2), (2, –2), (2, 3), (–1, 3)
Area of a rectangle.
A = bh
Substitute 3 for b and 5 for h.
A = 3 • 5
A = 15 units2

15. Additional Example 2B: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
(0, 0), (5, 0), (6, 4), (1, 4)
Area of a parallelogram.
A = bh
Substitute 5 for b and 4 for h.
A = 5 • 4
A = 20 units2

16. Substitute 4 for b and 5 for h.
Check It Out: Example 2A
Graph the figure with the given vertices. Then find the area of the figure.
(–3, –2), (1, –2), (1, 3), (–3, 3) x y
(–3, –2)
(1, –2)
(1, 3)
(–3, 3) 4 5
Area of a rectangle.
A = bh
Substitute 4 for b and 5 for h.
A = 4 • 5
A = 20 units2

17. Area of a parallelogram.
Check It Out: Example 2B
Graph the figure with the given vertices. Then find the area of the figure.
(–1, –1), (3, –1), (5, 3), (1, 3)
(5, 3) x y
(–1, –1)
(3, –1)
(1, 3) 4
Area of a parallelogram.
A = bh
Substitute 4 for b and 4 for h.
A = 4 • 4
A = 16 units2

18. Additional Example 3: Estimating Area Using Composite Figures
Use a composite figure to estimate the shaded area.
Draw a composite figure that approximates the irregular shape. Divide the composite figures into simple shapes.
Area of larger rectangle:
A = bh = 2 • 4 = 8
Area of smaller rectangle:
A = bh = 1 • 2.5 = 2.5
The shaded area is approximately 10.5 square units.

19. Check It Out: Example 3
Use a composite figure to estimate the shaded area.
Draw a composite figure that approximates the irregular shape. Divide the composite figures into simple shapes.
Area of larger rectangle:
A = bh = 3 • 4 = 12
Area of smaller rectangle:
A = bh = 2 • 4 = 8
The shaded area is approximately 20 square units.

20. Additional Example 4: Finding Area and Perimeter of a Composite Figure
Find the perimeter and area of the figure. 6 6 3 3 6 5 5
The length of the side that is not labeled is the same as the sum of the lengths of the sides opposite, 18 units.
P =
= 52 units

21. Additional Example 4 Continued6 6 3 3 6 5 5
A = 6 • • • 5
Add the areas together. =
= 72 units2

22. Find the perimeter of the figure.
Check It Out: Example 4
Find the perimeter of the figure.
The length of the side that is not labeled is 2. 2 4 6 7 7 2 6 2
P = ?
= 42 units 4

23. Check It Out: Example 4 Continued2
Find the area of the figure. 4 6 7
Add the areas together.
A = 2 • • • • 2 7 2 2 6 = 2 2
= 38 units2 2 6 4 2 4 7 2 2 + + +

24. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 24

25. Lesson Quiz: Part I
1. Find the perimeter of the figure.
44 ft
2. Find the area of the figure.
108 ft2

26. Lesson Quiz: Part II
Graph the figure with the given vertices and find its area.
3. (–4, 2), (6, 2), (6, –3), (–4, –3)
50 units2

27. Lesson Quiz: Part III
Graph the figure with the given vertices and find its area.
4. (4, –2), (–2, –2), (–3, 5), (3, 5)
42 units2

28. Lesson Quiz for Student Response Systems
1. Identify the perimeter of the figure.
A. 34 feet
B. 32 feet
C. 30 feet
D. 28 feet 28

29. Lesson Quiz for Student Response Systems
2. Identify the area of the figure.
A. 32 in2
B. 34 in2
C. 38 in2
D. 44 in2 29