Engage New York Module 7
Geometry and Measurement Word Problems
Use this study guide to prepare for your Mid-Module Assessment.
The assessment will be given on _________________. You should be
familiar with all topics covered in this study guide.
Geometric Shapes & Their Attributes:
When we look at geometric shapes, we should be able to talk about the
attributes those shapes have. An attribute is the characteristic of a given
shape. For example, you may describe a shape’s size, shape, color, or number
of sides.
Let’s see if we can identify some shapes that have parallel sides. Parallel sides
means two sides that will never cross paths.
 Which shapes shown have two
sets of parallel sides?
 Which shapes only have one set
of parallel sides?
 Which shapes have no parallel
sides?
The rectangle, square, and rhombus all
have two pairs of parallel sides.
The trapezoid only has one pair (the top and the bottom).
The triangle has no pairs of parallel sides. Were you able to identify this
attribute on your own?
Now look at the shapes again? Which shapes have the attribute of being foursided? Right! The rectangle, the rhombus, the square, and the trapezoid all
have four sides. This means that they are quadrilaterals! Quadrilaterals are
shapes with four sides!
Constructing Shapes with Given Attributes:
What if I gave you a list of attributes and asked you to construct the shape with
a ruler and a pencil? Do you think you could do this? Let’s try it together! Let’s
use the attributes in the box to construct a shape.
Attributes
four right angles
four straight sides
two pairs of
parallel sides
Your turn: try tw0 more! Use the attributes given to construct your shapes.
Attributes
Attributes
no right angles
no sides equal in length
four sides
four straight sides
no pairs of parallel
sides
one pair of parallel sides
Understanding Perimeter:
Perimeter is the measure of the outside edge of a closed geometric shape.
Think of a fence that goes around a yard…if we measured that fence, we
would have the perimeter of the yard.
To find the perimeter of a geometric shape, we need
to measure the length of each side and then add all
of the sides together. Look at the example. To find
the perimeter of this rectangle, we would add
10 + 4 + 10 + 4. What is the perimeter of the rectangle?
Sometimes, with larger and more complex
shapes, it is helpful to solve for the perimeter
by chunking. Look at the shape to the right.
There are several ways we can “chunk” this.
Maybe we want to add all the A’s first. There
are 3 A’s all worth 5 ft. So, I can solve for the
A’s by multiplying 3 and 5 to get 15. I can also
do this with the B’s (4 x 3 = 12). Then I will add 15 + 12 + 11 to find my perimeter.
What is the perimeter of the shape?
It is a good idea to “chunk” pieces together because it is easier to add together
less numbers than a whole bunch of numbers. In our example above, we
chunked it into 3 numbers…which is easier to handle than 8 numbers!
Understanding Rectangles:
On this assessment you will also have to apply your understanding of rectangles.
Remember:
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Rectangles are four sided shapes
They have all right angles
Opposite sides are parallel
Opposite sides are equal in length
You can use this information to find the perimeter of irregular
shapes even when all of the side lengths are not given.
Look at the image to the right. Let’s say that the dotted line
represents where I want to build a fence. How much fencing would I need to purchase?
Even though I am missing one of the sides where I want to place fencing, I can still figure out
the length of the missing side. I can use the lengths of the other sides to help me.
If I imagine the shape to be a complete rectangle, I know that the length of the missing side
must be equal to the total length of its opposite side.
Use your finger to find the side that is opposite your missing side. You should see that the
opposite side is broken into two pieces: a 2 ft. piece and a 6 ft. piece. You need to combine
these to get the length of your missing side. The length of your missing side is 8 ft.
Now you can calculate the amount of fencing that is needed. Calculate the amount of
fencing needed.
Name: ___________________
Practice Test:
1. Look at the shapes shown below.
a. Circle all of the shapes that have four right angles.
b. Place an X on all of the shapes that have at least one pair of parallel sides.
2. Name all of the shapes from above that are NOT quadrilaterals. Tell how you know that
they are not a quadrilateral.
3. Use your ruler and a pencil to construct a trapezoid using triangles. Label the side lengths
of your shape.
4. Draw a shape that has two right angles, four sides, and no sides of the same length.
5. I need to build a rectangular shaped fence around my swimming pool. The fence will be 12
feet long and 7 feet wide. How many feet of fencing will I need to buy? Draw a picture and
write an equation that proves your answer.
4. Find the perimeters of the irregular shapes. Pay attention to any missing sides.
perimeter = ________
perimeter = ________
5. How many more meters is the perimeter of the second shape than the first shape? Write
an equation and then solve.
6. A farmer wants to separate his animals into two pens of equal size and shape with a
walkway that goes between the two pens as shown in the picture. He has fencing for the
first pen. He needs to purchase fencing for the walkway and the other pen. How much
fencing will the farmer have to buy? Show your work.