Rectangle Puzzle: Perimeter Calculation With Squares

Hey guys, let's dive into a fun geometry problem! We're going to use five squares, each with a side length of 4 cm, to build a rectangle. Then, we'll figure out the perimeter of that rectangle. Sounds cool, right? This is a classic type of problem that helps us understand how shapes fit together and how to calculate their measurements. We'll break it down step by step, so even if geometry isn't your favorite, you'll be able to follow along and get the answer. The core idea is to visualize how these squares can be arranged to form a rectangle and then use the side lengths to find the perimeter. Perimeter, remember, is just the total distance around the outside of a shape. So, grab your thinking caps, and let's get started! We will focus on making sure we understand the core concepts and formulas needed for the problem. Remember, the most crucial step in approaching any geometry problem is to visualize the situation. If you can see how the squares can be arranged, you're halfway to the solution.

Understanding the Problem and Setting Up

Alright, so the first thing we need to do is fully understand the problem. We have five squares, and each has sides of 4 cm. Imagine these little squares, all identical in size. Now, the challenge is to put them together in a way that creates a rectangle. The question wants us to find the perimeter of the rectangle we construct. Before we even think about the math, let's think about how we can arrange these squares. There are a few ways to do this, but the most straightforward is to lay them out in a row. This creates a long, thin rectangle. However, we could also stack some on top of each other to get a different configuration. The key here is to consider all possible arrangements. For our purposes, the most efficient is to arrange the squares in a straight line, because it makes the calculations easier. When we do this, we know that the length of the rectangle will be longer than the width. But, let's not jump ahead; we'll figure out the exact dimensions soon. The perimeter of a rectangle is calculated using the formula: Perimeter = 2 * (length + width). This formula is super important, so make sure you remember it! We will use this formula to find the answer, it is not that hard. By understanding the basics, you can solve complex problems easily.

Visualizing the Rectangle and Finding Its Dimensions

Now, let's picture our rectangle. We know we're using five squares, each with sides of 4 cm. If we arrange these squares side by side in a single row, the length of the rectangle will be determined by the combined lengths of the sides of these squares. Since each square has a side length of 4 cm, and we are using five of them, the length of the rectangle will be 5 * 4 cm = 20 cm. Got it? Good. Now, what about the width? The width of the rectangle will be the same as the side of one of the squares. Since each square has a side of 4 cm, the width of the rectangle will also be 4 cm. So, our rectangle will be 20 cm long and 4 cm wide. Imagine those squares lined up. This gives us the dimensions we need to calculate the perimeter. The key is to see how the squares connect to form the larger shape. By carefully considering the side lengths of each square, you can easily calculate the dimensions of the rectangle.

Now that we have the dimensions, it's time to plug these values into the perimeter formula. Remember, the formula is Perimeter = 2 * (length + width). Substituting the values we found, we get: Perimeter = 2 * (20 cm + 4 cm). When you solve this you should obtain the solution easily.

Calculating the Perimeter and Final Answer

Okay, we've got the dimensions of our rectangle: a length of 20 cm and a width of 4 cm. Now, let's put those numbers into the perimeter formula: Perimeter = 2 * (length + width). So, Perimeter = 2 * (20 cm + 4 cm). First, you add the length and the width, which is 20 cm + 4 cm = 24 cm. Then, multiply that sum by 2: 2 * 24 cm = 48 cm. And there you have it! The perimeter of the rectangle is 48 cm. That's the total distance around the outside of the rectangle formed by the five squares. Calculating the perimeter is the final step, but it relies on everything we've done so far. From understanding the problem to visualizing the rectangle and finding its dimensions, each step is crucial. By following the process, you not only solve the problem but also strengthen your understanding of geometric concepts and problem-solving skills. Remember, with a little bit of practice, these problems become much easier. Congrats, guys, you did it!

In conclusion, we started with five squares, each with a side of 4 cm. We arranged them to form a rectangle, where the length was 20 cm (5 squares * 4 cm/square) and the width was 4 cm. Using the perimeter formula (2 * (length + width)), we found the perimeter to be 48 cm. The process demonstrated how to use basic geometric concepts to solve a practical problem. This exercise helps in understanding shapes, dimensions, and how to apply formulas. Well done, you have successfully navigated the problem!