Multi-Sports Court Area Calculation: A Step-by-Step Guide

Hey guys! Let's dive into a classic math problem that might just pop up on your ENEM exam. This one involves calculating areas, and it's super practical because it deals with real-world scenarios like sports courts. We're going to break down how to find the total area of a multi-sports court, given the dimensions of a volleyball court inside it and the fraction of the total area that the volleyball court occupies. So, grab your thinking caps, and let's get started!

Understanding the Problem

Okay, so the heart of the problem lies in understanding the relationship between the volleyball court's area and the total area of the multi-sports court. We know the volleyball court is a rectangle, and we're given its width (9 meters) and length (18 meters). We also know that this volleyball court takes up 1/4 of the entire multi-sports court's area. The big question is: How do we use this information to find the total area? The solution is based on two main steps: First, calculate the area of the volleyball court using its dimensions. Second, since the volleyball court area represents 1/4 of the total area, use this fraction to find the full area of the multi-sports court. This involves using some basic algebra and a bit of logical thinking. It's a pretty common type of problem, especially in exams like ENEM, because it tests your ability to apply math to real-world situations. So, let’s break it down piece by piece to make sure we’ve got a solid grasp on the method. Remember, the key here is to stay calm, read the problem carefully, and identify what information you have and what you need to find. With that in mind, let’s move on to the calculations!

Step 1: Calculate the Area of the Volleyball Court

The first thing we need to do, guys, is figure out the area of the rectangular volleyball court. Remember your geometry? The area of a rectangle is simply its length multiplied by its width. In this case, the volleyball court is 9 meters wide and 18 meters long. So, to find its area, we just multiply these two numbers together. This is a fundamental concept in area calculations, and it’s super important to get this part right because it's the foundation for the rest of the problem. So, let’s write it down: Area = Length × Width. Now, let’s plug in the numbers we have: Area = 18 meters × 9 meters. When you multiply 18 by 9, you get 162. So, the area of the volleyball court is 162 square meters. Don't forget the units! We're talking about area, so it's square meters, not just meters. This step is crucial because it gives us a concrete value to work with. We now know the size of the volleyball court, and we know it represents a fraction of the total area we're trying to find. Think of it like a piece of a puzzle – we've got one piece down, and now we need to use it to see the bigger picture. With the area of the volleyball court calculated, we're ready to move on to the next step and use that information to find the total area of the multi-sports court. Let's keep going!

Step 2: Determine the Total Area of the Multi-Sports Court

Alright, we've nailed the area of the volleyball court – it's 162 square meters. Now, the problem tells us that this area represents 1/4 (one-fourth) of the total area of the multi-sports court. This is the crucial piece of information that will help us solve the puzzle! So, what does it mean when something is 1/4 of a whole? It means that the whole is four times bigger than that part. In our case, the total area of the multi-sports court is four times the area of the volleyball court. To find the total area, we just need to multiply the volleyball court's area by 4. It’s like saying if 162 square meters is one slice of a pie, and the pie is cut into four slices, then we need to figure out the size of the whole pie. So, let’s do the math: Total Area = 4 × Area of Volleyball Court. We know the area of the volleyball court is 162 square meters, so let's plug that in: Total Area = 4 × 162 square meters. When you multiply 162 by 4, you get 648. So, the total area of the multi-sports court is 648 square meters. And that’s it! We’ve found our answer. This step is all about understanding the relationship between the part and the whole and using that knowledge to scale up to the total area. By breaking it down like this, you can tackle similar problems with confidence. Next up, we'll recap our steps and highlight some key takeaways to make sure you've got this concept down pat.

Final Answer and Key Takeaways

Okay, guys, let's recap what we've done and make sure we're crystal clear on the solution. We started with a multi-sports court that had a rectangular volleyball court inside. We knew the volleyball court measured 9 meters by 18 meters, and it occupied 1/4 of the total area of the multi-sports court. Our mission was to find the total area of the multi-sports court. First, we calculated the area of the volleyball court by multiplying its length and width: 18 meters × 9 meters = 162 square meters. Then, we used the fact that the volleyball court's area represents 1/4 of the total area. To find the total area, we multiplied the volleyball court's area by 4: 4 × 162 square meters = 648 square meters. So, the final answer is that the total area of the multi-sports court is 648 square meters. Key Takeaways:

• Always read the problem carefully and identify what information you have and what you need to find.
• Remember the formula for the area of a rectangle: Area = Length × Width.
• Understand fractions and how they relate to the whole. If you know a part and the fraction it represents, you can find the whole.
• Pay attention to units! Area is measured in square units.

This type of problem is a classic example of how math can be applied to real-world situations. By breaking it down into smaller steps, it becomes much easier to solve. Practice similar problems, and you'll become a pro at area calculations in no time! If you found this helpful, keep practicing, and you’ll ace those exams! Remember, math is like a muscle – the more you use it, the stronger it gets. Keep up the great work, and I'll see you in the next explanation!"