# Lesson 5

Areas of Parallelograms

### Problem 1

Select **all** segments that could represent a corresponding height if the side \(m\) is the base.

e

f

g

h

j

k

n

### Solution

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### Problem 2

Find the area of each parallelogram.

### Solution

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### Problem 3

Find the area of each parallelogram.

### Solution

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### 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?

### Solution

### Problem 5

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.

### Solution

### 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.

- 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?

### Solution

### Problem 7

Find the area of the shaded region. All measurements are in centimeters. Show your reasoning.