1. 6-1 Warm Up Problem of the Day Lesson Presentation
Perimeter & Area of Rectangles & Parallelograms
6-1
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Pre-Algebra
6-1
Perimeter & Area of Rectangles & Parallelograms
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
A. 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. The formula for the perimeter of a rectangle can be written as P = 2b + 2h, where b is the length of the base and h is the height.
Helpful Hint

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

10. Try This: Example 1A
A. 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. Try This: Example 1B
B. 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.

14. Additional Example 2A: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
A. (–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. The height of a parallelogram is not the length of its slanted side
The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base.
Helpful Hint

16. Additional Example 2B: Using a Graph to Find Area
Graph the figure with the given vertices. Then find the area of the figure.
B. (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

17. A = bh A = 4 • 5 A = 20 units2 Try This: Example 2A
Graph the figure with the given vertices. Then find the area of the figure.
A. (–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

18. A = bh A = 4 • 4 A = 16 units2 Try This: Example 2B
Graph the figure with the given vertices. Then find the area of the figure.
B. (–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

19. Additional Example 3: 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

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

21. Find the perimeter of the figure.
Try This: Example 3
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

22. Try This: Example 3 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 + + +

23. Lesson Quiz: Part 1
1. Find the perimeter of the figure.
12 ft
5 ft
5 ft
4 ft
5 ft
5 ft
44 ft
12 ft

24. Lesson Quiz: Part 2
2. Find the area of the figure.
12 ft
5 ft
5 ft
4 ft
5 ft
5 ft
108 ft2
12 ft

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

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