In the beginning of this lesson, several students modeled their handcrafted objects as polygons. This practice can have several applications. For example, assume you want to know how many students will fit on a dance floor. You could model the students as polygons, determine the area of those polygons, and then calculate how many polygons will fit within the area of the dance floor. As another example, perhaps you want to know if a small sofa will fit in the back of the family sport utility vehicle. You could model the sofa and the vehicle as polygons and compare their areas. Watch the following video to see a few examples of how you could apply this new skill.
As you watch this video, use the study guide to follow along if you'd like. Click the button below to download the study guide.
In this video, we will consider how to use the area of polygons in real-life situations. In this first example, we are told that a friend of yours is hosting a party and wants to know if they have enough room for everyone to fit on a dance floor if it is only 15 feet long and 12 feet wide. Assuming that each person needs a space 3 feet wide and 3 feet long in which to dance; can we fit 25 people on the dance floor? A good place to start is to determine the area of the dance floor and the amount of area needed for each person to dance. The area of the floor is found by multiplying fifteen by twelve to obtain an area of 180 square feet. The area each person needs is equal to three times three, or 9 square feet. By dividing the total area by the area needed for each person, or 180 by 9, we can determine the number of people that can fit in this space… Unfortunately there is only room for twenty people, not twenty-five.
In problem #2 we are told that the cargo space of an enclosed trailer is 5 feet wide and 8 feet long. Can it fit 3 benches that are two feet wide and six feet long without stacking them on themselves? If we use the same technique as in problem #1 we find the area of the floor of the cargo trailer is five times eight or 40 square feet, and the area of each bench is 2 by 6 which is only twelve square feet. By dividing the area of trailer by the area needed for each bench, it looks like we should be able to fit all three of those benches. However, this calculation can be a bit deceiving. Let's look at this diagram for example… The cargo space is 5 feet wide and 8 feet long, but each of the benches is two feet wide and 6 feet long. Even though the calculated area is large enough to fit three benches, the physical constraints won't allow it. It is always important to model your space with a diagram before committing to an answer for a real-life scenario.
Let's look at one more problem. Here, we are told that a slug of steel can be rolled into a sheet that is 987 square inches. Could we create a panel for a door that is 2 feet wide and 3 feet tall? A slug of steel is simply a large, thick piece of steel that hasn't been manufactured into a usable form. Supposing that this slug can be rolled into a sheet of any shape that covers 987 square inches, we should be able to determine whether a sheet can be formed to fit a panel that is two feet wide and three feet long. Before we complete any math though, it is a good idea to convert our measurements to the same units. We can convert in either direction – feet to inches, or inches to feet – in this case I think we would like to convert the dimensions of the door from feet into inches. So two feet is the same as twenty-four inches, and three feet is the same as thirty-six inches. So, the dimensions of this panel result in an area of 864 square inches. It appears that yes we can roll this slug of steel into a sheet that can produce a panel for the door.
Question
Based on the examples in the video, what's one way to determine the area of an everyday object?
