Trapezoid Area: Calculate With Bases 28m & 120m, Height 4m

Hey guys! Ever wondered how to calculate the area of a trapezoid? Don't worry, it's easier than it looks! Let's dive into it with a real-world example. In this guide, we'll break down the process step-by-step, ensuring you not only understand the formula but also how to apply it. We'll tackle a specific problem involving a trapezoid with given base lengths and height, and by the end, you'll be a trapezoid area calculating pro!

Understanding the Trapezoid and Its Area

Before we jump into calculations, let's quickly recap what a trapezoid is. A trapezoid is a four-sided shape (a quadrilateral) with at least one pair of parallel sides. These parallel sides are called the bases (often denoted as b1 and b2), and the perpendicular distance between these bases is the height (h). Understanding these components is crucial because the area of a trapezoid depends directly on these measurements. The formula for the area of a trapezoid is given by: Area = (1/2) * (b1 + b2) * h. This formula might seem intimidating at first, but we'll break it down to see how simple it truly is. We're essentially finding the average length of the bases and multiplying it by the height. This method works because a trapezoid can be visualized as a combination of a rectangle and one or two triangles, and this formula effectively captures the total area of these shapes combined. So, let's get started with our problem and see how this formula works in practice!

The Problem: Finding the Area

Our problem involves a trapezoid with the following measurements: one base (b1) is 28 meters, another base (b2) is 120 meters, and the height (h) is 4 meters. We're given four possible answers and our task is to determine the correct area. Let's recap the formula: Area = (1/2) * (b1 + b2) * h. The key to solving any mathematical problem is to correctly identify the given values and the formula to use. In this case, we have all the necessary values – the lengths of both bases and the height – and we know the formula for calculating the area of a trapezoid. The next step is simply plugging these values into the formula and performing the calculation. This is where attention to detail comes in handy to avoid simple arithmetic errors. Now, let’s replace the variables in the formula with the values provided in the problem and move towards finding the solution. Remember, mathematics isn't about memorizing formulas but understanding how and why they work.

Step-by-Step Calculation

Alright, let’s plug in the values and calculate the area step by step. First, we have the formula: Area = (1/2) * (b1 + b2) * h. Now, let's substitute b1 with 28 meters, b2 with 120 meters, and h with 4 meters. Our equation now looks like this: Area = (1/2) * (28 + 120) * 4. The next step is to perform the addition inside the parentheses: 28 + 120 = 148. So, the equation becomes: Area = (1/2) * 148 * 4. Now, we can multiply 148 by 4, which gives us 592. The equation is now: Area = (1/2) * 592. Finally, we multiply 592 by 1/2 (or divide by 2), which gives us 296. So, the calculated area is 296 square meters. It's essential to remember the units. Since the lengths were given in meters, the area is in square meters. We have successfully found the area using our formula and the given measurements. But wait! Something seems off. Let's double-check our calculations and compare our result with the provided options.

Checking Our Work and Finding the Correct Answer

Okay, we arrived at 296 square meters, but that's not one of the options (a) 80m, b) 120m, c) 90m, d) 100m. This is a crucial step: always check your work! It's easy to make a small mistake. Let’s quickly review our calculations. We added 28 and 120 correctly to get 148. We then multiplied 148 by 4, which indeed equals 592. And finally, we divided 592 by 2, resulting in 296. So, the math seems correct. However, the provided answer choices don't match our result. This discrepancy indicates a possible error in the provided options or the problem statement itself. In real-world scenarios, this is a common situation, and it’s important to recognize when your calculated answer doesn't align with the given choices. In such cases, it's a good practice to re-evaluate the problem and the given information to identify any potential errors or misinterpretations. This could mean re-reading the problem statement, checking the provided measurements, or even confirming the answer choices. In this specific scenario, since our calculations are accurate, it's likely that the error lies within the provided options.

Since our calculation yielded 296 square meters and this option isn't available, we should highlight this discrepancy. It’s possible there was a mistake in the options provided. However, the core process of calculating the area of a trapezoid remains the same. Let’s recap the key takeaways from this exercise.

Key Takeaways and the Importance of Double-Checking

So, guys, we've successfully walked through calculating the area of a trapezoid! The key takeaway here is understanding the formula: Area = (1/2) * (b1 + b2) * h. We learned how to identify the bases and the height, plug those values into the formula, and perform the calculation. But even more importantly, we learned the value of double-checking our work. In this case, our calculations were correct, but the answer wasn't among the provided choices. This highlights a critical skill in mathematics and in life: verifying your results and questioning discrepancies. Remember, mathematics isn't just about getting the right answer; it's about understanding the process and being able to identify when something doesn't add up. Always ensure your answer makes sense in the context of the problem. In this situation, we correctly applied the formula and arrived at a logical answer. The next step would be to communicate the discrepancy if this were a test or assignment. So keep practicing, and you'll become a trapezoid-calculating whiz in no time!

I hope this guide has made calculating the area of a trapezoid clearer and more approachable for you. Keep practicing, and you'll ace those geometry problems in no time! Remember, it's all about understanding the formula and applying it step-by-step. You've got this!