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6-8 Accelerated 7 Unit 6 Lesson 10

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Accelerated 6 •Accelerated 7

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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 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 6, Lesson 10

Decomposing Bases for Area

Accelerated 7

Practice

Problem 1

You find a crystal in the shape of a prism. Find the volume of the crystal.

The point \(B\) is directly underneath point \(E\), and the following lengths are known:

From \(A\) to \(B\): 2 mm
From \(B\) to \(C\): 3 mm
From \(A\) to \(F\): 6 mm
From \(B\) to \(E\): 10 mm
From \(C\) to \(D\): 7 mm
From \(A\) to \(G\): 4 mm

An irregular pentagonal prism with base A, F, E, D, C. Segment A, G indicates the height of the prism. Point B lies between A and C.

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Lesson 10 Resources

Student Materials

Problem 2

This carved wooden jewelry box is from Indonesia. The base of the box is an octagon with each side 4.2 cm long. The box is 9 cm tall. What is the volume of the box?

A photo of a decorative wooden box.

An octagon.

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Problem 3

ForLesson 16: Drawing Triangles (Part 1)

A triangle has one side that is 7 cm long and another side that is 3 cm long.

Sketch this triangle and label your sketch with the given measurements. (If you are stuck, try using a compass or cutting some straws to these two lengths.)
Draw one more triangle with these measurements that is not identical to your first triangle.
Explain how you can tell they are not identical.

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Problem 4

ForLesson 12: Alternate Interior Angles

Select all equations that represent a relationship between angles in the figure.

Three points intersect to form 6 lines. Clockwise, the angles measure b degrees, 30 degrees, 90 degrees, a, degrees, c degrees, blank.

\(90-30=b\)
\(30+b=a+c\)
\(a+c+30+b=180\)
\(a=30\)
\(a=c=30\)
\(90+a+c=180\)

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Problem 5

ForLesson 8: Slopes Don't Have to Be Positive

Match each graph of a linear relationship to a situation that most reasonably reflects its context.

A graph of a line labeled A. — A

A graph of a line labeled B. — B

A graph of a line labeled C. — C

A graph of a line labeled D. — D

Graph A
Graph B
Graph C
Graph D

\(y\) is the weight of a kitten \(x\) days after birth.
\(y\) is the distance left to go in a car ride after \(x\) hours of driving at a constant rate toward its destination.
\(y\) is the temperature, in degrees \(C\), of a gas being warmed in a laboratory experiment.
\(y\) is the height in feet climbed after walking up \(x\) stairs.

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