 # Area of Parallelograms

Videos and solutions to help Grade 6 students find the area formula for the region bounded by a parallelogram by composing it into rectangles. They understand that the area of a parallelogram is the area of the region bounded by the parallelogram.

New York State Common Core Math Module 5, Grade 6, Lesson 1

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Opening Exercise

Name each shape.

A rectangle is considered a parallelogram, but is commonly called a rectangle because it is a more specific name.

Discussion

Cut out a parallelogram and how can we change the parallelogram into a rectangle.

Lesson Summary

The formula to calculate the area of a parallelogram is A = bh, where b represents the base and h represents the height of the parallelogram.

The height of a parallelogram is the line segment perpendicular to the base. The height is drawn from a vertex that is opposite the base.

Lesson 1 Exercises

1. Find the area of each parallelogram below. Each figure is not drawn to scale.

2. Draw and label the height of each parallelogram. Use the correct mathematical tool to measure (in inches) the base and height, and calculate the area of each parallelogram.

3. If the area of a parallelogram is 35/42 cm2 and the height is 1/7 cm, cm, write an equation that relates the height, base, and area of the parallelogram. Solve the equation. Explore why the formula A = bh is used for rectangles and parallelograms.

Calculate the area of each parallelogram. The figures are not drawn to scale.
Questions 4 and 5. Problem Set
1 - 2. Draw and label the height of each parallelogram.

3 - 6. Calculate the area of each parallelogram. The figures are not drawn to scale.

7. Brittany and Sid were both asked to draw the height of a parallelogram. Their answers are below.
Are both Brittany and Sid correct? If not, who is correct? Explain your answer.

8. Do the rectangle and parallelogram below have the same area? Explain why or why not.

9. A parallelogram has an area of 20.3 cm^2 and a base of 2.5 cm. Write an equation that relates the area to the base and height, h. Solve the equation to determine the height of the parallelogram.

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