# Lesson 5

Bases and Heights of Parallelograms

Let’s investigate the area of parallelograms some more.

### Problem 1

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

A:

A

B:

B

C:

C

D:

D

### Problem 2

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

Draw a segment showing the height corresponding to that base.

### Problem 3

Find the area of each parallelogram.

### Problem 4

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

A:

6 units

B:

4.8 units

C:

4 units

D:

5 units

### Problem 5

Find the area of each parallelogram.

### Problem 6

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

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

### 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.

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