Lesson 5

Bases and Heights of Parallelograms

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Problem 1

Select all parallelograms that have a correct height labeled for the given base.

4 parallelograms on a grid, labeled A, B, C, D.
A:

A

B:

B

C:

C

D:

D

Solution

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Problem 2

The side labeled \(b\) has been chosen as the base for this parallelogram.

parallelogram on a grid. base = 4 units, distance from bottom side to top side = 2 units. Left and right sides are slanted.

Draw a segment showing the height corresponding to that base.

Solution

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Problem 3

Find the area of each parallelogram.

3 parallelograms on a grid, labeled A, B, C.

Solution

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Problem 4

If the side that is 6 units long is the base of this parallelogram, what is its corresponding height?

Parallelogram. 

A:

6 units

B:

4.8 units

C:

4 units

D:

5 units

Solution

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Problem 5

Find the area of each parallelogram.

3 parallelograms labeled A, B, C. 

 

Solution

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Problem 6

Do you agree with each of these statements? Explain your reasoning.

  1. A parallelogram has six sides.
  2. Opposite sides of a parallelogram are parallel.
  3. A parallelogram can have one pair or two pairs of parallel sides. 
  4. All sides of a parallelogram have the same length.
  5. All angles of a parallelogram have the same measure. 

Solution

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(From Unit 1, Lesson 4.)

Problem 7

A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.

  1. What is the area, in square meters, of 6 triangles? If you get stuck, consider drawing a diagram.
  2. How many triangles are needed to compose a region that is \(1\frac 12\) square meters?

Solution

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(From Unit 1, Lesson 2.)