Lesson 5

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

e

f

g

h

j

k

n

Find the area of each parallelogram.

Find the area of each parallelogram.

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?

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. 

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?

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