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6-8 Grade 6 Unit 1 Lesson 6

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K-5 Math •6-8 Math 9-12 Math

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•Grade 6 Grade 7 Grade 8

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 •Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19

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Unit 1, Lesson 6

Area of Parallelograms

Grade 6

Practice

Problem 1
Student Task Statement
Which three of these parallelograms have the same area as each other?

Four parallelograms, labeled A, B, C, and D. Figure A, the top and bottom sides each 5 units, slanted sides descend 3 units and move right 1 unit. Figure B, the top and bottom sides are each 3 units, slanted sides ascend 5 units while moving right 6 units. Figure C is a square of 4 units on each side. Figure D, the left and right sides are each 3 units, and the top and bottom sides descend 1 unit as they move right 5 units.

A

B

C

D
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Lesson 6 Resources

Student Materials Student Materials in Spanish

Problem 2

Student Task Statement

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

,
,
,
,

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Problem 3

Student Task Statement

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

A: 10 square units

Parallelogram A, right side = 5 units, height = question mark.<br>

B: 21 square units

Parallelogram B, bottom side = question mark. Right triangle drawn outside of parallelogram, base = 1 unit, height = 7 units.

C: 25 square units

Parallelogram C, bottom side = question mark. Right triangle drawn outside of parallelogram, base = 2.5 units, height = 5 units.

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Problem 4

Student Task Statement

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

<p>A photograph of the Dockland Building in Hamburg, Germany. The building is shaped like a parallelogram.</p>

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?

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Problem 5

ForLesson 5: Bases and Heights of Parallelograms

Student Task Statement

Select all segments that could represent a corresponding height if the side 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.

e
f
g
h
j
k
n

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Problem 6

ForLesson 3: Reasoning to Find Area

Student Task Statement

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.

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