Calculate Perimeter And Area Of A Rectangle One Side Is 72 Cm

Hey guys! Today, we're diving into the world of geometry to tackle a classic problem: calculating the perimeter and area of a rectangle. Specifically, we're dealing with a rectangle where one side is 72 cm, and the other side is three times smaller. Sounds interesting, right? Let's break it down step by step so you can conquer this problem and similar ones with confidence. We will explore the fundamental concepts and formulas needed to calculate these essential properties of rectangles. So, grab your calculators and let’s get started!

Understanding the Basics: Rectangles, Perimeter, and Area

Before we jump into the calculations, let's make sure we're all on the same page with the basics. A rectangle, as you probably know, is a four-sided shape (a quadrilateral) where all angles are right angles (90 degrees). Think of it like a perfectly shaped box or a door. The opposite sides of a rectangle are equal in length. We usually refer to these sides as the length and the width.

Now, what about perimeter? Imagine you're walking around the edge of the rectangle. The total distance you walk is the perimeter. In other words, the perimeter is the sum of the lengths of all the sides. For a rectangle, this means adding up the length, the width, the length again, and the width again. We can express this as a formula: Perimeter = 2 * (length + width). This formula is a cornerstone in geometry, and understanding it is crucial for solving many problems. The perimeter is a linear measurement, so it's measured in units of length, such as centimeters (cm), meters (m), or inches (in).

Next up, area. Think of area as the amount of space inside the rectangle. If you were painting the rectangle, the area would be the amount of paint you need to cover the entire surface. The area of a rectangle is calculated by multiplying its length by its width: Area = length * width. The area is a two-dimensional measurement, so it's measured in square units, such as square centimeters (cm²), square meters (m²), or square inches (in²). Mastering the concept of area allows you to quantify the size of surfaces, which is incredibly useful in various real-world applications, from construction to interior design.

Understanding these basic concepts – what a rectangle is, how to calculate its perimeter, and how to calculate its area – is the key to solving our problem. We'll use these formulas and definitions to find the perimeter and area of our specific rectangle.

Step 1: Finding the Length of the Other Side

Okay, so we know one side of our rectangle is 72 cm. The problem tells us that the other side is three times smaller. What does that mean? It means we need to divide the length of the known side by 3 to find the length of the other side. Guys, pay close attention to these keywords! "Three times smaller" is a classic way geometry problems try to trick you. Always double-check what the problem is really asking.

So, let's do the math: 72 cm / 3 = 24 cm. This means the other side of our rectangle is 24 cm long. Now we have both the length and the width of the rectangle. We're one step closer to finding the perimeter and area. This step highlights the importance of careful reading and interpretation of the problem statement. Misunderstanding the relationship between the sides can lead to incorrect calculations. Therefore, taking the time to fully grasp the given information is a crucial skill in problem-solving.

Step 2: Calculating the Perimeter

Remember our perimeter formula? It's Perimeter = 2 * (length + width). We now know the length is 72 cm and the width is 24 cm. Let's plug those values into the formula:

Perimeter = 2 * (72 cm + 24 cm)

First, we need to add the length and width: 72 cm + 24 cm = 96 cm

Now, we multiply that sum by 2: 2 * 96 cm = 192 cm

So, the perimeter of our rectangle is 192 cm. Awesome! We've calculated the distance around the rectangle. Remember, the perimeter is a linear measurement, so our answer is in centimeters, not square centimeters. This step demonstrates the application of a formula to solve a problem. By substituting the known values into the perimeter formula, we can systematically arrive at the solution. Understanding the order of operations (addition before multiplication) is essential for accurate calculations.

Step 3: Calculating the Area

Time for area! The formula for area is Area = length * width. We already know the length (72 cm) and the width (24 cm). Let's plug those in:

Area = 72 cm * 24 cm

Now, we multiply: 72 * 24 = 1728

So, the area of our rectangle is 1728 square centimeters (cm²). Fantastic! We've calculated the space inside the rectangle. Remember, area is a two-dimensional measurement, so our answer is in square centimeters. This final calculation reinforces the understanding of the area formula and its application. The result, 1728 cm², represents the amount of surface enclosed within the rectangle. This is a fundamental concept in various fields, including construction, design, and everyday problem-solving.

Putting It All Together: The Solution

Alright, guys, we've done it! We've successfully calculated the perimeter and area of the rectangle. To recap:

• The perimeter of the rectangle is 192 cm.
• The area of the rectangle is 1728 cm².

We started by understanding the basic concepts of rectangles, perimeter, and area. Then, we carefully broke down the problem into smaller, manageable steps. We found the length of the other side, calculated the perimeter using the perimeter formula, and calculated the area using the area formula. This step-by-step approach is key to solving geometry problems and many other types of problems as well. By breaking down a complex problem into smaller parts, you can tackle each part individually and then combine the results to find the overall solution. This strategy promotes clarity and reduces the likelihood of errors.

Practice Makes Perfect: Further Exploration

Now that you've mastered this problem, why not try some similar ones? You can change the length of one side or the factor by which the other side is smaller or larger. Try calculating the perimeter and area of squares, too! Remember, a square is just a special type of rectangle where all sides are equal. Geometry is all about practice, so the more you work with these concepts, the more comfortable and confident you'll become. Exploring variations of the problem helps to solidify your understanding of the underlying principles. By changing the parameters, you can test your knowledge and develop a deeper appreciation for the relationships between different geometric properties. This proactive approach is essential for mastering geometry and applying it to real-world scenarios.

Keep practicing, and you'll be a geometry whiz in no time! Understanding how to calculate perimeter and area isn't just about solving textbook problems; it's a valuable skill that can be applied in many real-life situations. From measuring a room for carpeting to designing a garden, the principles of geometry are all around us. So, embrace the challenge, enjoy the process, and keep exploring the fascinating world of geometry!