Mastering the Cost of Fencing a Hexagonal Field

A farmer plans to install fencing around a hexagonal field with each side measuring 320 feet. What will be the total cost of fencing if it is priced at $1.75 per foot?

• A. $2,240
• B. $2,800
• C. $3,360
• D. $4,480

Answer: (C)

To determine the total cost of fencing the hexagonal field, we first need to calculate the perimeter of the field. A hexagon has six equal sides, so we multiply the length of one side by the total number of sides. Given that each side measures 320 feet, the perimeter calculation is as follows: Perimeter = number of sides × length of each side Perimeter = 6 × 320 feet Perimeter = 1,920 feet Next, to find the total cost of the fencing, we multiply the perimeter by the cost per foot. The fencing costs $1.75 per foot, so the calculation is: Total Cost = Perimeter × Cost per foot Total Cost = 1,920 feet × $1.75/foot Total Cost = $3,360 Therefore, the total cost of fencing the hexagonal field is $3,360. This confirms that the option stating $3,360 is the correct and accurate answer, as it correctly reflects the total expenditure needed based on the dimensions of the field and the cost per foot of the fencing.

When tackling the TEAS ATI Mathematics Practice Test, it’s always good to stay sharp on essential concepts—like calculating costs effectively! Today, let’s delve into a practical problem involving fencing a hexagonal field. Why hexagons? Well, they’re not just neat shapes—they’re common in landscaping and garden designs, and understanding how to handle such calculations can prepare you for real-world scenarios.

Let’s set the stage: Imagine you're a farmer looking to fence in your land. This field has six equal sides, each measuring 320 feet. We want to figure out the total cost of fencing this field if the fencing costs $1.75 per foot. Sounds like a well-rounded math problem that's straight out of your future—so, let’s break it down step-by-step!

The Hexagon’s Perimeter: What’s the Deal?

First things first, we need to find the perimeter of the hexagonal field. Knowing that a hexagon has six sides, we'll use a simple formula:

Perimeter = number of sides × length of each side.

With our numbers plugged in:

Perimeter = 6 × 320 feet.

Now, when you do the math, you’ll find:

Perimeter = 1,920 feet.

Got that? Great! Knowing the perimeter helps you paint the full picture here—it's like putting the frame around an artwork, creating structure before diving into the details. Speaking of details, let’s talk costs!

Show Me the Money: Calculating the Total Cost

Now that we know how much fencing we’ll need, it's time to see how much that'll pinch our wallets. Remember, the fencing costs $1.75 per foot. Here’s where multiplication comes into play for the total cost:

Total Cost = Perimeter × Cost per foot.

Plugging in what we’ve calculated:

Total Cost = 1,920 feet × $1.75/foot.

Doing this calculation leads us right to:

Total Cost = $3,360.

There you have it—the total cost of fencing your hexagonal field is $3,360. Which answer choice is that? Oh, that's right, it’s (C) $3,360—an excellent fit for your budgeting plan!

Why Does This Matter for the TEAS?

Many students might not realize it, but understanding these kinds of calculations isn’t just about the numbers. It demonstrates your ability to translate word problems into numeric solutions. You’ll find similar scenarios on the TEAS ATI Mathematics Test that test your comprehension and practical math skills, so knowing how to approach these can really set you apart.

As you're preparing for your tests, think about these applications. How might budgeting for a project or calculating distances come up in your future career? This isn’t just math; it’s preparing you for real-world challenges!

Wrapping It Up

So next time you face a fencing project (or just a math problem), remember this—break it down to find your perimeter and calculate your costs. You’ll not only ace your TEAS but also walk away with skills that will serve you well in your journey through life, be it farming, construction, or even planning your next DIY home project.

Math can feel daunting, but with a little approach and practice, you can master it! Ready to tackle the next problem? Let’s go! You got this.