Area of a Parallelogram

1. Area of a Parallelogram 6.3.1.2 Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

2. I can… • Determine the area of parallelograms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

3. Finding the Area of Parallelograms Parallelograms In this lesson, we will learn how to find the area of parallelograms. Parallelograms are quadrilaterals that have two sets of opposite parallel sides. These sides are parallel. These sides are also parallel. So, this is a parallelogram. This quadrilateral is also a parallelogram. These sides are parallel. And these sides are also parallel. Here is one more quadrilateral. These sides are parallel. And these sides are also parallel. So, this quadrilateral is also a parallelogram.

4. Finding the Area of Parallelograms Let’s use a grid to help us see unit squares. What is the area of this parallelogram?

5. Finding the Area of Parallelograms We can find the area by counting. 1 2 3 4 4 ½ 5 5 ½ 6

6. Finding the Area of Parallelograms 6 square units The area of the parallelogram is 6 square units. Let’s decompose and rearrange the parallelogram. Now, we can see 6 whole square units.

7. Finding the Area of Parallelograms 6 square units

8. Finding the Area of Parallelograms Now, let’s find the area of this parallelogram.

9. Finding the Area of Parallelograms 9 square units Again, we’ll use a grid to help us see square units. Notice that this time, there are parts of the parallelogram that are neither whole units nor half units. So let’s decompose the shape and rearrange the parts to help us see complete unit squares. What is the area of the shape? 9 square units

10. Finding the Area of Parallelograms 9 square units The area of the parallelogram is 9 square units.

11. Finding the Area of Parallelograms Now, let’s find the area of this parallelogram.

12. Finding the Area of Parallelograms 12 square units Again, we’ll use a grid to help us see square units. So, let’s decompose the shape and rearrange the parts to help us see complete unit squares. What is the area of the shape? 12 square units

13. Finding the Area of Parallelograms Area of a Parallelogram = Base × Height 12 square units 4 units 3 units We know the area is 12 square units. We can use a formula to find the area of a parallelogram. The area is equal to its base times its height. The base of this parallelogram is 3 units. Its height is 4 units. 3 x 4 = 12. The area is 12 square units.

14. Finding the Area of Parallelograms 15 square units Here is a new parallelogram. We can decompose it to find its area. What is the area? 15 square units

15. Finding the Area of Parallelograms 15 square units 5 units 3 units Notice that 15 square units is equal to multiplying the base—which is 3 units … … by the height—which is 5 units. The area of the parallelogram is 15 square units.

16. Finding the Area of Parallelograms 30 square units Let’s find the area of this parallelogram. What is the area? 30 square units

17. Finding the Area of Parallelograms 30 square units 6 units 5 units 5 units … … times 6 units is equal to 30 square units. The area of the parallelogram is 30 square units.

18. Finding the Area of Parallelograms 20 square feet 5 feet 4 feet Area of a Parallelogram = Base × Height This parallelogram has a base that measures 4 feet … … and a height of 5 feet. What is its area? 20 square feet Let’s find the area of this parallelogram.

19. Finding the Area of Parallelograms 54 square m 6 m 9 m Area of a Parallelogram = Base × Height It has a base of 9 meters … … and a height of 6 meters. What is its area? 54 square meters Let’s find the area of this parallelogram.

20. Finding the Area of Parallelograms 21 square feet 7 feet 3 feet Area of a Parallelogram = Base × Height It has a base of 3 feet … … and a height of 7 feet. What is its area? 21 square feet Let’s find the area of this parallelogram.

21. Finding the Area of Parallelograms 88 square cm 8 cm 11 cm Area of a Parallelogram = Base × Height Its base is 11 cm … … and its height is 8 cm. What is the area? 88 square cm Let’s find the area of this parallelogram.

22. Finding the Area of Parallelograms 12 square feet 5 feet 3 feet 4 feet Area of a Parallelogram = Base × Height Sometimes, you might see more measurements than you need to find the area. Here are three measurements. But we only need the base and the height to find the area. This measurement is an important one, but it is not needed to find the area of the parallelogram. The base is 4 feet … … and the height is 3 feet. Notice that the height is perpendicular to the base. Now, what is the area? 12 square feet

23. Finding the Area of Parallelograms Lightning Round

24. Finding the Area of Parallelograms What is the area of the parallelogram? 48 square cm 6 cm 7 cm 8 cm

25. Finding the Area of Parallelograms What is the area of the parallelogram? 180 square m 9 m 11 m 20 m

26. Finding the Area of Parallelograms What is the area of the parallelogram? 90 square km 15 km 18 cm 6 km

27. Finding the Area of Parallelograms The area of a parallelogram is 45 square centimeters and the height is 9 centimeters. What is the base? A = bh 45 = b • h 45 = b • 9 9 9 5 cm = b

28. Finding the Area of Parallelograms The area of a parallelogram is 180 square feet and the height is 24 feet. What is the base? A = bh 180 = b • h 180 = b • 24 24 24 7.5 ft. = b

29. I can… • Determine the area of parallelograms Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

30. 10.1 Notes Area of a Parallelogram Area = base • height A = bh Copy the equation (don’t just solve in your head) Substitute the numbers for the variables Solve base