Now that you've seen several examples, can you determine if a real-life situation involves quadrilaterals? Read the scenario on each of the slides below and decide if a working knowledge of quadrilaterals would help solve the problem.
|
Suppose you have a summer job managing a pay-to-park parking lot downtown. People are complaining that your rectangular parking spaces are too narrow and that their cars are getting damaged when the people next to them open their car doors. You're starting to lose customers, so you decide to redraw the lines and make each space a little bigger. However, you need to figure out how many of the new larger spaces can fit in your lot--to see if you'll lose too much money by expanding the spaces. Does this situation involve the properties of quadrilaterals? Yes, it does. The parking spaces are rectangles, and you'll need to calculate the area of the new wider spaces and the area of the entire lot to figure out how many paying customers you'll have with the new arrangement.
Kill'em Dead Pest Control needs to provide an estimate to a building's owner, including how much bug spray will be needed to treat the entire area. The owner of the building has asked that the bug spray be applied to the outside of the building only, so it will just go along the bottom of all the walls. What parts of pest-control technician's problem can be solved using knowledge of quadrilaterals? What parts cannot? As you can see, the apartment building is shaped like a quadrilateral (a rectangle). An exterminator could easily calculate the perimeter of the rectangle. To estimate the amount of bug spray he or she would apply to the building, however, the exterminator would need knowledge of the rate of application and the cost of the bug spray and labor to provide an actual cost estimate.
Imagine you're super hungry and you decide to order a pizza. You see that Speedy Mama's Pizza has a special this week: You can buy a 12 inch pizza for $19.99 or a 20 inch pizza for $24.99. Can your knowledge of quadrilaterals help you decide which is better deal? You need more information. If the pizzas are round and the sizes represent diameters, then your knowledge of quadrilaterals will not help you. However, if the pizzas are rectangular, the sizes stand for a side length or a diagonal and understanding the properties of quadrilaterals can help you. As a birthday surprise, you decide to build a bookshelf for your mom's new home office. At some point, though, the project goes awry: What was supposed to be a 3 foot by 4 foot rectangular book shelf is now a lopsided parallelogram. If the shelf is going to hold books, that parallelogram needs to become a sturdy rectangle. Your grandmother provides some helpful advice: Use a metal brace to connect the opposite corners of the bookshelf.
What property of quadrilaterals can help you fix the problem? You can use your knowledge of the relationship between a rectangle's diagonals and its sides or angles to determine the best length for the metal brace, which will run from one corner of the rectangle to the other. |
 |
