5.3.4Practice:Modeling: Finding Parallelograms

Practice

Geometry Sem 1

With the lot you have chosen, your goal is to construct the largest possible dog park that meets the code restrictions.

Making Sense of the Problem

What do you know about the lot size and code requirements?

It's 350x300 feet

Has to have a 4 foot sidewalk around

On one end it has to have a parking lot 20 feet wide

Can not build anything 25 feet of the trees

It must be a parallelogram

What do you want to find out?

Is it a parallelogram

What kind of answer do you expect?

What size park can i build

Below is a map of the town:

1. Look at the theater on First Ave, between Alder and Birch. If the corners of the theater are all right angles, is the theater a parallelogram? Why or why not? Yes

A parallelogram is a quadrilateral is whose angles are all right angles

2. Look at the school on Second Ave, between Dogwood and Elm.

a) Is the school a quadrilateral? Why or why not? (1 point)

b) Is the school a parallelogram? Why or why not? (1 point)

Planning your dog park:

3. Draw a picture that represents what you know about the empty lot. (2 points)

4. Is the empty lot a parallelogram? Why or why not? (2 points)

5. Where are you going to put the parking lot? Draw the parking lot on your map and label its dimensions. (2 points)

6. Is your parking lot a parallelogram? (2 points)

7. Draw in the dimensions of the zone restricted by the creek or trees. (1 point)

8. Draw in the sidewalk and its dimensions. (2 points)

Solving the Problem:

9. What are the final dimensions of the largest dog park you can create on your lot (not including the sidewalk or the parking lot)? Use the Quadrilateral Tool located in the activity to help you. (2 points

10. Most importantly, to satisfy the mayor, is this space a parallelogram? Why or why not? (1 point)

11. Draw a sketch of your dog park. Correctly label the dimensions that prove your dog park is a parallelogram. (2 points)