# Lesson 5

Areas of Parallelograms

### Problem 1

Select all segments that could represent a corresponding height if the side $$m$$ is the base.

A:

e

B:

f

C:

g

D:

h

E:

j

F:

k

G:

n

### Problem 2

Find the area of each parallelogram.

### Problem 3

Find the area of each parallelogram.

### Problem 4

The Dockland Building in Hamburg, Germany is shaped like a parallelogram.

If the length of the building is 86 meters and its height is 55 meters, what is the area of this face of the building?

### Problem 5

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

(From Unit 1, Lesson 4.)

### Problem 6

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?