On the previous page, you saw how a good working knowledge of quadrilaterals can help you save money. But what other real-life problems require a geometry solution based on the properties of quadrilaterals? And how can you recognize these situations?
One of the first steps, of course, is to look for a quadrilateral. Then, ask yourself what information is missing. Would finding the area or perimeter of the quadrilateral help you solve the problem? Is the solution represented by a missing side length or a missing angle? Let's look at some examples and try applying these criteria to each situation. Study the problem on each of the tabs below.
Example 1
Example 2
Example 3
Example 4
To earn a little extra money, Manny decides to raise pepper plants and sell the peppers in his uncle's booth at the local farmers' market. After a little research, Manny learns that each pepper plant needs 8 square feet of growing space to thrive and produce the greatest quantity and quality of peppers. Manny builds 10 raised-bed gardens that are 4 feet wide and 12 feet long.
When Many goes to the nursery to buy pepper plants, he wants to make sure that he buys exactly the number of pepper plants he needs. If he buys too many, the nursery will not let him return the extra. If he buys too few, he wastes gas money and time making another trip. How can Manny solve his problem? Will his knowledge of quadrilaterals help?
| What information is needed to solve Manny's problem? | Many needs to know the total area of growing space in all 10 of his raised beds. Once he knows the total number of square feet, Manny can divide that number by 8 to figure out how many pepper plants he needs to purchase. |
| What shapes are involved in this problem? Can you use your knowledge of quadrilaterals to find the needed information? | The raised bed gardens form rectangles. To find the total area of the beds, Manny can use the area formula for a rectangle and basic multiplication skills. |
Quincy saved most of the money from his summer job to purchase a new flat-screen television for the basement game room where he often plays video games and watches movies with his friends. Quincy is thinking of purchasing a 30-inch TV because that size is on sale at the nearest electronics story, according to the television commercials he's been seeing.
Quincy knows that 30 inches refers to the diagonal length of the TV, but he wants to know how wide the screen is. Will it fit inside the entertainment center his grandmother passed along to him, or will he have to buy a new piece of furniture as well?
| What information is needed to solve Quincy's problem? | Quincy needs to know how the diagonal length of the screen relates to the width of the screen. To figure that out, he also needs to know the aspect ratio. |
| What shapes are involved in Quincy's problem? Can you use your knowledge of quadrilaterals to find the needed information? | Flat screen televisions are rectangular in shape. You can use your knowledge of the relationship between diagonal length and side length to figure out how wide the screen is. |
The Silver Fox Hotel in Springfield, where Tabitha works as an event planner, is hosting a banquet. Tabitha has to decide how many people to seat at each table and then have her team put the chairs in place.
If the hotel's tables have a radius of 10 feet and each person needs about 3 feet of personal space to sit comfortably, how many people can sit at one table?
What information does Tabitha need? Can her knowledge of quadrilaterals help her find that information?
No, unfortunately not. Quadrilaterals don't have a radius, but circles do. If Tabitha remembers what she learned about circles in geometry class, she can easily figure out how many "slices" she needs to divide each table into.
Carmela wants to design a kite for next month's kite festival. She knows that the shape of the kite largely determines how well it will fly. Carmela builds a model kite and begins to measure its sides and angles carefully. However, before she can measure the last two angles, her protractor snaps into several pieces!
Can Carmela calculate the measurements of the remaining angles using what she learned about quadrilaterals from geometry class, or does she have to go out and buy a new protractor?
| What information does Carmela need? | Carmela needs to find the missing angles on her model kite so that she can construct a full-size kite for the festival. |
| What shape is at the center of Carmela's problem? What does she need to know about this shape's properties to solve the problem? | The shape involved is a kite, a type of quadrilateral. If Carmela remembers what she learned about the angle sums of a quadrilateral and the relationships between the angles of a kite, she can figure out the measures of the last two angles. |
