Section B Practice Problems

Problem 1

What is the perimeter of this rhombus? Explain or show your reasoning.
Diego says he can find the area of this rectangle because he knows 2 side lengths.

Do you agree with Diego? Explain your reasoning.

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Solution

52 cm. Sample response: The shape is a rhombus, so all sides are 13 cm. $4 \times 13 = 52$
No. Sample response: Diego doesn't have enough information. He knows two side lengths but needs one of the other two side lengths to find the perimeter. There is no information that he can use to find those lengths.

Problem 2

The spinning part of a windmill is called a rotor. This figure represents a rotor with 5 blades.

Draw the lines of symmetry for the figure.
Each blade is 5 feet long and $1 \frac{1}{2}$ feet wide. What is the perimeter of the rotor, as shown in the diagram? Explain or show your reasoning.

image of shape that looks like a windmill with 5 blades. Each blade, rectangle, length 5 feet, width 1 and 1 half feet. Center is pentagon.

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Solution

Drawing shows lines going through each vertex of the pentagon in the middle and the middle of the opposite side.
$57 \frac{1}{2}$ feet. Sample response: The perimeter of each blade is $5 + 5 + 1 \frac{1}{2}$ or $11\frac{1}{2}$ feet. There are 5 of these blades, so that's $5 \times 11 \frac{1}{2}$ . I know that $5 \times 11 = 55$ and then $\frac{5}{2}$ more makes $57 \frac{1}{2}$ .

Problem 3

Here is Rectangle R.

What shape can be folded once along a line of symmetry to create R? What are the side lengths of that unfolded shape?
What shape can be folded twice along lines of symmetry to create R? What are the side lengths of that unfolded shape?

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Solution

A 30 cm by 21cm rectangle or a 15 cm by 42 cm rectangle
A 60 cm by 21 cm rectangle, a 30 cm by 42 cm rectangle, or a 15 cm by 84 cm rectangle

Problem 4

How many lines of symmetry are there in this design? Explain or show your reasoning.

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Solution

Sample response: There are 16 parts that repeat and look symmetric. Any line going through the middle of those parts is a line of symmetry and there are 8 of them. Any line going between adjacent shapes is a line of symmetry and there are 8 of those, making 16 different lines of symmetry.

Problem 5

Make a shape or design with 1 or more lines of symmetry. Trade shapes with a partner and find all the lines of symmetry of your partner's shape. You may find pattern blocks helpful to make your shape or design.

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Solution

Sample response:

The figure has 6 lines of symmetry. There are 3 lines that go through the centers of opposite triangles and there are 3 more lines of symmetry that go through the centers of opposite squares.