Lesson 5

Areas of Parallelograms

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Problem 1

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

A parallelogram with a bottom side labeled m and a right side labeled n. Dashed lines e, f, j, and k are drawn perpendicular to side m, and dashed lines g and h are drawn perpendicular to side n.
A:

e

B:

f

C:

g

D:

h

E:

j

F:

k

G:

n

Solution

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Problem 2

Find the area of each parallelogram.

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

Solution

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Problem 3

Find the area of each parallelogram.

3 parallelograms labeled A, B, C. 

 

Solution

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Problem 4

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

A photograph of the Dockland Building in Hamburg, Germany. The building 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

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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

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(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?

Solution

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(From Unit 1, Lesson 2.)

Problem 7

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

A shaded rectangle located at an angle within a larger rectangle. 

Solution

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(From Unit 1, Lesson 3.)