Lesson 6

Area of Parallelograms

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Problem 1

Which three of these parallelograms have the same area as each other?

Four parallelograms, labeled A, B, C, and D.
A:

A

B:

B

C:

C

D:

D

Solution

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Problem 2

Which pair of base and height produces the greatest area? All measurements are in centimeters.

A:

\(b = 4\), \(h=3.5\)

B:

\(b = 0.8\), \(h=20\)

C:

\(b = 6\), \(h=2.25\)

D:

\(b = 10\), \(h=1.4\)

Solution

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Problem 3

Here are the areas of three parallelograms. Use them to find the missing length (labeled with a "?") on each parallelogram.

A: 10 square units

B: 21 square units

C: 25 square units

Three 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

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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(From Unit 1, Lesson 5.)

Problem 6

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.)