Calculating Rectangle Area: A Step-by-Step Guide
Hey guys! Let's dive into a fun math problem. We're going to figure out the area of a rectangle. You know, those shapes that are everywhere – think of your phone, a table, or even a door! This particular rectangle has a length of 4.9 decimeters (dm), and its width is a bit of a mystery, but we know it's 2.7 dm smaller than the length. Don't worry, it's not as tricky as it sounds. We'll break it down step by step, making sure everyone understands. This is a classic geometry problem, perfect for anyone brushing up on their math skills or just starting out. Understanding how to calculate the area is super useful in everyday life. Whether you're figuring out how much paint you need for a wall or estimating the size of a garden, the concept of area is your friend. So, grab your pencils and let's get started. We'll go through each step carefully, so you won't miss a thing. The goal is not just to get the answer but to really grasp the process of solving such problems. Ready? Let's go!
Step 1: Understanding the Problem and Identifying the Knowns
Alright, first things first, let's make sure we totally get the problem. We're given a rectangle, and we need to find its area. Remember, the area is the amount of space inside the shape. Now, what do we know? We know the length of the rectangle is 4.9 dm. That's one piece of the puzzle! The problem also tells us something about the width. It's not directly given, but we know it is 2.7 dm less than the length. This means the width is shorter than the length by that amount. Making sure we understand what is given to us is crucial. Let's write down what we know: Length = 4.9 dm; Width = Length - 2.7 dm. This is the foundation upon which we'll build our solution. It's like having all the ingredients before you start baking a cake. Without these key pieces of information, we would be lost, unable to even begin. So, make sure you always start by clearly identifying what you know from the start. That way, the subsequent calculations will be easy to understand. Got it? We know the length, and we know how the width relates to the length. Great, let's move on!
Breaking Down the Knowns
Let's really zoom in on what we know. The length, 4.9 dm, is straightforward. But the width needs a little more work. The problem states that the width is 2.7 dm smaller than the length. That means we have to subtract 2.7 dm from the length to find the width. This is where a little bit of subtraction comes in. It's important to grasp that the words in the problem give us clues about what to do. The phrase "2.7 dm smaller" is a signal to subtract. We're basically comparing the width to the length and defining how they differ. Think of it like a puzzle; each piece of information is a piece, and understanding how the pieces fit is the key to solving it. So, we're not just looking at numbers; we're interpreting the relationships between them. The more we break down the problem like this, the easier it becomes. This step is about converting the words into a mathematical action, subtraction in this case. Keep in mind that understanding what the problem tells you is as important as the math itself. Now that we've broken down what we know, we are ready to move on. Let's calculate the width in the next step!
Step 2: Calculating the Width of the Rectangle
Alright, time to find the width! We've already established that the width is 2.7 dm less than the length. That means we have to subtract 2.7 dm from the length (4.9 dm). Here's how it looks mathematically: Width = Length - 2.7 dm. Now, let's plug in the length value: Width = 4.9 dm - 2.7 dm. Now, do the subtraction, which is pretty straightforward. 4.9 minus 2.7 equals 2.2. So, the width of the rectangle is 2.2 dm. See? Not so hard, right? We've successfully calculated the width by using the information we were given and performing a simple subtraction. It's like following a recipe; once you have all the ingredients (the length and the relationship between length and width), you can follow the instructions (the subtraction) to get the final result (the width). This step is crucial because we need both the length and the width to calculate the area. Now we have two key pieces of information – the length (4.9 dm) and the width (2.2 dm). We're making great progress! We're nearly ready to calculate the area, which is our ultimate goal.
The Subtraction Process
Let's go over the subtraction step to make sure everyone is on the same page. We have 4.9 and we need to subtract 2.7. Think of it this way: 9 tenths minus 7 tenths equals 2 tenths. Then, 4 minus 2 equals 2. Put it all together, and you get 2.2. Remember, the decimal point is important! It keeps everything in the correct place value. If you want to visualize it, imagine having 4 whole units and 9 little pieces, then taking away 2 whole units and 7 little pieces. What's left is 2 whole units and 2 little pieces, or 2.2. Subtraction is a fundamental math skill, and it's essential for solving this problem. Taking your time and double-checking your work is always a good idea. This is not a race; it's about making sure we get the correct answer. Now, we are ready to move on, and put our knowledge to work.
Step 3: Calculating the Area of the Rectangle
We're now ready for the main event: calculating the area! Remember, the area of a rectangle is found by multiplying its length by its width. The formula is: Area = Length * Width. We already know both the length and the width. The length is 4.9 dm, and the width is 2.2 dm. So, let's plug those values into our formula: Area = 4.9 dm * 2.2 dm. Now, we just need to multiply these two numbers. Doing the multiplication, 4.9 times 2.2 gives us 10.78. But don't forget the units! Since we're dealing with area, our units are square decimeters (dm²). Therefore, the area of the rectangle is 10.78 dm². We've successfully calculated the area! High five! This step combines everything we've learned so far: understanding the problem, identifying the knowns, calculating the width, and now, finally, the area. It showcases the practical application of basic math principles in a simple, straightforward way. Calculating area is a fundamental skill in geometry. Whether you're figuring out how much paint you need for a wall or estimating the size of a garden, the concept of area is your friend. This is why we need to master the calculation.
Multiplying Decimals
Let's break down that multiplication step. We need to multiply 4.9 by 2.2. First, ignore the decimal points for a moment and multiply 49 by 22. You can do this by hand using standard multiplication, or use a calculator if you're allowed. 49 times 22 equals 1078. Now, remember the decimal points? Count how many digits are after the decimal point in both of your original numbers. In 4.9, there's one digit after the decimal (the 9). In 2.2, there's also one digit after the decimal (the 2). So, in total, there are two digits after the decimal point. Therefore, in your answer (1078), you need to place the decimal point so that there are two digits after it. That means the answer is 10.78. Simple, right? Always remember to count those decimal places! They are critical for accurate answers. Multiplying decimals is a skill that comes with practice. The more you do it, the easier it gets. The key is to be organized and methodical.
Step 4: Stating the Final Answer
We've reached the final step! We've done all the calculations, and we have our answer. Let's state the final answer clearly and completely. The area of the rectangle is 10.78 square decimeters (10.78 dm²). Make sure your answer is complete - always include the units! Units are really important; they tell us what the number actually represents. Without them, the number is meaningless. Imagine saying you have 10.78, without specifying what it is. Is it inches? Feet? Decimeters? We wouldn't know! So, always include the units. In our case, the units are square decimeters (dm²). This tells us that we're talking about an area, specifically the area of a rectangle, and that we have measured the sides in decimeters. Now, we can pat ourselves on the back. You've successfully found the area of the rectangle! Awesome work, everyone! The whole exercise reinforces not just mathematical ability but also logical thinking and attention to detail. Great job on sticking with it! We have not only found the correct answer, but have also completely understood the process of finding the area of the rectangle.
Summarizing the Solution
Let's quickly recap what we did: 1. We understood the problem and identified the length and the relationship between the length and width. 2. We calculated the width by subtracting 2.7 dm from the length (4.9 dm). 3. We used the formula Area = Length * Width. 4. We plugged in the values (4.9 dm * 2.2 dm) and got 10.78 dm². 5. We stated our final answer: The area of the rectangle is 10.78 square decimeters (10.78 dm²). This is the key: to always break down problems into manageable steps. This is a super handy approach for all sorts of math problems, not just area calculations. If you can break a complicated problem into smaller, simpler parts, you can solve anything. Just make sure you understand each step, take your time, and double-check your work. You're well on your way to becoming a math whiz! Congratulations on completing this problem! You now have a solid understanding of how to find the area of a rectangle. Keep practicing, and you'll get even better!