Unit 4, Lesson 14
Fractional Lengths in Triangles and Prisms
Grade 6
14.1
Warm-up
Find the area of Triangle A in square centimeters.
Show your reasoning.
A triangle labeled A with a vertical side. One vertex is to the left of the vertical side. A dashed horizontal line is drawn from the first vertex to the vertical side of the triangle and a right angle symbol is indicated. The dashed line and the vertical side are both labeled 4 and one half centimeters.
14.2
Activity
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The area of Triangle B is 8 square units. Find the length of . Show your reasoning.
A triangle labeled B has a horizontal side on the bottom of the triangle and a vertex above the horizontal side. A dashed line is drawn from the vertex to the horizontal sideand a right angle symbol is indicated. The horizontal side is labeled lowercase b and the dashed line is labeled eight thirds. -
The area of Triangle C is square units.
What is the length of ? Show your reasoning.A triangle labeled C has a horizontal side at the top of the triangle and a vertex below the horizontal side and to the left. A horizontal line extends from the horizontal side and to the left. A vertical dashed line is drawn from the bottom vertex to the extended horizontal line and a right angle symbol is indicated. The dashed line is labeled h and the horizontal side of the triangle is labeled 3 and three fifths.
14.3
Activity
Your teacher will give you cubes that have edge lengths of inch.
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Here is a drawing of a cube with edge lengths of 1 inch.
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How many cubes with edge lengths of inch are needed to fill this cube?
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What is the volume, in cubic inches, of a cube with edge lengths of inch? Explain or show your reasoning.
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- Four cubes are piled in a single stack to make a prism. Each cube has an edge length of inch. Sketch the prism, and find its volume in cubic inches.
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Use cubes with an edge length of inch to build prisms with the lengths, widths, and heights shown in the table.
For each prism, record in the table how many -inch cubes can be packed into the prism and the volume of the prism.
prism
length (in)prism
width (in)prism
height (in)number of -inch
cubes in prismvolume of
prism (in3)1 1 2 1 2 2 1 4 2 5 4 2 5 4
Student Lesson Summary
If a rectangular prism has edge lengths of 2 units, 3 units, and 5 units, we can think of it as 2 layers of unit cubes, with each layer having unit cubes in it. So the volume, in cubic units, is:
To find the volume of a rectangular prism with fractional edge lengths, we can think of it as being built of cubes that have a unit fraction for their edge length. For instance, if we build a prism that is -inch tall, -inch wide, and 4 inches long using cubes with a -inch edge length, we would have:
- A height of 1 cube, because .
- A width of 3 cubes, because .
- A length of 8 cubes, because .
The volume of the prism would be , which is 24 cubic units.
How do we find its volume in cubic inches? We know that each cube with a -inch edge length has a volume of cubic inch, because . Since the prism is built using 24 of these cubes, its volume, in cubic inches, would then be , which is 3 cubic inches.
The volume of the prism, in cubic inches, can also be found by multiplying the fractional edge lengths in inches:
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