1. Preview
Warm Up
California Standards
Lesson Presentation

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. California
Standards
MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
Also covered: MG2.2, MG2.4, and MG3.2

4. Vocabulary
perimeter
area
base
height
composite figure

5. Perimeter is the distance around a polygon
Perimeter is the distance around a polygon. To find the perimeter of any polygon, you add the lengths of all its sides.
Since opposite sides of a parallelogram are equal in length, you can find a formula for the perimeter of a parallelogram.
P = w + l + w + l
= w + w + l + l
= 2w + 2l w l

7. Additional Example 1: Finding the Perimeter of Parallelograms
A. Find the perimeter of the figure. 5 14
P = 2w + 2l
Perimeter of a parallelogram.
= 2(5) + 2(14)
Substitute 5 for w and 14 for l.
= = 38 units

8. Additional Example 1: Finding the Perimeter of Parallelograms
B. Find the perimeter of the figure. 20 16
P = 2w + 2l
Perimeter of a parallelogram.
= 2(16) + 2(20)
Substitute 16 for w and 20 for l.
= = 72 units

9. Check It Out! Example 1
A. Find the perimeter of the figure. 6 11
P = 2w + 2l
Perimeter of a parallelogram.
= 2(6) + 2(11)
Substitute 6 for w and 11 for l.
= = 34 units

10. Check It Out! Example 1
B. Find the perimeter of the figure. 5 13
P = 2w + 2l
Perimeter of a parallelogram.
= 2(5) + 2(13)
Substitute 5 for w and 13 for l.
= = 36 units

11. The area of a plane figure is the number of unit squares needed to cover the figure. The base of a parallelogram is the length of one side. The height is the perpendicular distance from the base to the opposite side.
Height
Side
Base

12. While perimeter is expressed in linear units, such as inches (in
While perimeter is expressed in linear units, such as inches (in.) or meters (m), area is expressed in square units, such as square feet (ft2).
You can cut a parallelogram and shift the cut piece to form a rectangle whose base and height are the same as those of the original parallelogram. The same number of unit squares are needed to cover the two figures. So a parallelogram and a rectangle that have the same base and height have the same area.

14. Since the base and height of a rectangle are the same as its length and width, the formula for the area of a rectangle can also be written as A = lw.
Helpful Hint

15. Additional Example 2: Using a Graph to Find Area
Graph and find the area of the figure with the given vertices.
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

16. 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.
Caution!

17. Additional Example 2: Using a Graph to Find Area
Graph and find the area of the figure with the given vertices.
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

18. Graph and find the area of the figure with the given vertices.
Check It Out! Example 2
Graph and find the area of the figure with the given vertices.
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

19. Area of a parallelogram.
Check It Out! Example 2
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

20. A composite figure is made up of basic geometric shapes such as rectangles, triangles, trapezoids, and circles. To find the area of a composite figure, find the areas of the geometric shapes and then add the areas.

21. 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

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

23. Find the perimeter of the figure.
Check It Out! 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

24. Check It Out! 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 + + +

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 and find the area of each figure with the given vertices.
3. (–4, 2), (6, 2), (6, –3), (–4, –3)
50 units2

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