The Quadrilateral Olympics Problem Set

The Quadrilateral Olympics have finally arrived. Use your knowledge of the properties of quadrilaterals to answer the following questions. Round all of your answers to the nearest tenth. Be sure to include the property or properties you used to answer each question.

The Pool

In a nod to the most common type of quadrilateral, this year’s Olympic organizers have designed the competitive swimming pool in the shape of a parallelogram. The largest corner of the pool has an angle measure of 135°. The length of the pool is 200 meters and the width 80 meters.

1. What is the measure of the smaller corner of the pool?
2. What is the perimeter of the pool?
3. What property or properties did you use to answer these questions?
   
   

The Ring

The announcer begins the preliminary round of the Women’s Olympic Boxing event. Standing in the center of the square boxing ring, he estimates that the length to the corner of the boxing ring is 10 feet.

4. What is the measure of one side of the boxing ring?
5. What is the perimeter?
6. What is the area?
7. What property or properties did you use to answer these questions?
   
   

The Floor Routine

You enter the gymnastics stadium and view the large rectangular mat used for the upcoming gymnastic floor routines. You notice that the width of the mat is 30 feet, marked off in 5-foot increments. There is a 67-foot banner that runs from one corner of the mat to the opposite corner.

8. What is the length of the mat?
9. What is the area of the mat?
10. What property or properties did you use to answer these questions?
    
    

The Podium

It is time for the medal round and you have front row seats! Directly in front of you are three podiums, each in the shape of a trapezoid. As you look closer, you notice that they are isosceles trapezoids and that the three podiums are similar to one another.

11. What does similar mean?
12. Curious about the trapezoids, you measure the top base angles and find them to be 130° on all three podiums. What is the measure of the bottom base angles?
13. What property or properties did you use to answer these questions?
    
    

The Medals

The awards ceremony has begun. You notice that this year’s medals have a new design and are rhombus shaped. The announcer lifts the medal and describes the medal as having diagonals of 4 inches and 6 inches.

14. What are the measures of the sides of the rhombus?
15. What property or properties did you use to answer these questions?
    

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