Unraveling The Fabric Puzzle: Calculating The Original Area

Hey there, math enthusiasts! Let's dive into a fun geometry problem that Laura encountered. This problem involves a rectangular piece of fabric and some clever cutting. We'll break down the question step-by-step and figure out the solution together. This is a classic example of how understanding area and basic multiplication can help you solve real-world problems. So, grab your pencils and let's get started on solving Laura's fabric puzzle! This is a great exercise for understanding area calculations and applying them to practical situations. We will focus on how to calculate the area of the rectangles and how to use the information given in the question to solve for the unknown area. This type of problem is designed to build your problem-solving skills and enhance your understanding of mathematical concepts. Remember, practice is key. The more problems you solve, the more confident you'll become in tackling these types of questions. Let's make this fun and learn something new! Are you ready to unravel the mystery of Laura's fabric?

Understanding the Problem and Identifying Key Information

Alright, guys, let's break down the problem. Laura bought a rectangular piece of fabric. She then cut out 10 identical rectangles from it. Each of these smaller rectangles has a height of 1.5 meters and a base of 2 meters. The question asks us to find the area of the original piece of fabric. So, we need to connect the information about the smaller rectangles to figure out the dimensions of the original larger rectangle. It's like a puzzle where we have to use the pieces (the smaller rectangles) to reconstruct the whole picture (the original fabric). The core concept here is understanding how area works, which is the space inside a two-dimensional shape. In this case, we're working with rectangles, and the area of a rectangle is calculated by multiplying its length (base) by its width (height). Keep in mind that the area is always measured in square units (like square meters, in this case). So, the ultimate goal is to find the total area that was there before Laura started cutting. We'll have to consider all the pieces that were cut from the big piece to do this! It is important to read the question carefully and pay attention to details, such as the number of rectangles cut and their dimensions. Remember that careful reading and analysis are essential steps in solving any word problem. Let's move on to the next step, where we will calculate the area of the smaller rectangles.

Calculating the Area of a Single Small Rectangle

So, before we figure out the area of the original piece of fabric, we need to calculate the area of one of the small rectangles. We know that each small rectangle has a base of 2 meters and a height of 1.5 meters. To find the area of a rectangle, we simply multiply the base by the height. In this case, that means 2 meters * 1.5 meters. Let's do the math: 2 * 1.5 = 3 square meters. Therefore, each small rectangle has an area of 3 square meters. Understanding this step is crucial because it allows us to figure out the total area of all the small rectangles that were cut from the bigger one. We have successfully determined the area of each small rectangle. Remember, this is just one piece of the puzzle. We need to use this information to find the area of the big rectangle. The next step will focus on how to use the area of one small rectangle to help calculate the area of the original piece of fabric. The area of a rectangle is found by multiplying its base by its height. Remember to always include the unit, in this case, square meters.

Calculating the Total Area of All the Cut Rectangles

Now that we know the area of a single small rectangle, let's figure out the total area of all the rectangles Laura cut. We know she cut out 10 identical rectangles, and each has an area of 3 square meters. To find the total area, we multiply the area of one rectangle by the number of rectangles: 3 square meters/rectangle * 10 rectangles = 30 square meters. That means the total area of all the small rectangles Laura cut out is 30 square meters. It's like saying that the fabric Laura cut represents a total of 30 square meters of space. This calculation is a key step towards finding the area of the original fabric, because, as we will see, it directly translates into the area of the original piece. Therefore, the total area of all the small rectangles is the area that was used to create all the smaller rectangles. Remember that the original fabric was the source of all the small rectangles. Let's move on to the next step and find the area of the original piece of fabric.

Determining the Area of the Original Fabric

Here’s the fun part, guys! Since the 10 small rectangles were cut from the original piece of fabric, the total area of the small rectangles is equal to the area of the original fabric. Therefore, if the total area of the 10 small rectangles is 30 square meters, then the area of the original piece of fabric is also 30 square meters. So, the answer is option b) 30 m². That means that Laura's original piece of fabric took up an area of 30 square meters before she started cutting it. It is also important to note that the area of the original piece of fabric is equal to the sum of the areas of the small rectangles. This is an important concept in geometry and helps with understanding how shapes relate to each other. By using the information of the small rectangles, we were able to find the area of the original piece of fabric. Congratulations! We’ve solved the puzzle! Let’s summarize the steps that we followed in solving this problem.

Summarizing the Steps and the Answer

Let’s quickly recap the steps we took to solve this problem:

1. Understand the problem: We identified the knowns (the dimensions and number of the small rectangles) and the unknown (the area of the original fabric).
2. Calculate the area of a small rectangle: We multiplied the base (2 meters) by the height (1.5 meters) to get 3 square meters.
3. Calculate the total area of the cut rectangles: We multiplied the area of one rectangle (3 square meters) by the number of rectangles (10) to get 30 square meters.
4. Determine the area of the original fabric: Since the small rectangles were cut from the original fabric, the total area of the small rectangles is the area of the original fabric. Therefore, the answer is 30 square meters.

So, the correct answer is b) 30 m². Great job, everyone! You've successfully solved Laura's fabric puzzle! This problem demonstrates how to apply your knowledge of area and multiplication to solve a practical problem. Keep practicing these types of problems, and you'll become a geometry whiz in no time. If you got it right, give yourself a pat on the back. If you didn't, don't worry! Review the steps and try another similar problem. The important thing is that you're learning and having fun with math. Remember, practice makes perfect. You are now equipped with the knowledge to solve similar problems. Congratulations on solving this geometry problem! Keep practicing your skills and exploring the world of math!