Calculating The Cost Of Landscaping A Triangular Garden
Hey guys! Let's dive into a fun math problem that's all about gardens and money. We're going to figure out how much it costs to plant grass in a triangular garden. This is a classic geometry and math word problem that helps us understand area calculations and real-world applications of math, such as budgeting for home improvements or landscaping projects. We will break down the steps, use the correct formulas, and ensure the entire process is understandable so you can confidently solve similar problems. If you want to transform your own backyard, it's pretty important to know your math, right? So, let's get started and break down this problem step by step to determine the total cost.
Understanding the Problem: The Triangular Garden
Alright, so here's the deal. We have a garden, and it's not just any garden; it's a triangle. Specifically, it's an equilateral triangle, which means all three sides are equal, but the problem only provides the base and height, which is all we need! The base of our triangle is 20 meters long, and the height is 15 meters. Think of it like a slice of pizza or a yield sign. Now, this garden is going to be covered with grass. The cost? A cool Rp30,000.00 per square meter. Our main goal is to figure out the total cost of getting the whole garden green and grassy. To do that, we need to calculate the area of the triangle first. Then, we can multiply that area by the cost per square meter. It is pretty simple once you break it down into steps, right? Let's get to work!
To make sure we're on the right track, let's list down all the important information so we won't get lost in the middle of our calculations:
- Shape: Equilateral Triangle
- Base (alas): 20 meters
- Height (tinggi): 15 meters
- Cost per Square Meter: Rp30,000.00
Calculating the Area of a Triangle: The First Step
Okay, guys, first things first: we need to figure out the area of our triangular garden. The area is the amount of space inside the triangle that the grass will cover. Remember the formula for the area of a triangle? It's pretty straightforward:
Area = 0.5 * base * height
Or,
Area = (1/2) * base * height
It's as simple as that! We know the base is 20 meters and the height is 15 meters. Let's plug those numbers into the formula:
Area = 0.5 * 20 meters * 15 meters
Area = 10 meters * 15 meters
Area = 150 square meters
So, the area of our triangular garden is 150 square meters. That's how much space we need to cover with grass. Now we can proceed with determining the total cost of planting grass in the garden. This is where we will use the calculated area and multiply it by the cost per square meter of grass.
Determining the Total Cost: The Final Calculation
Alright, we've got the area of the garden: 150 square meters. We also know that the cost of grass is Rp30,000.00 per square meter. To find the total cost, we simply multiply the area by the cost per square meter:
Total Cost = Area * Cost per Square Meter
Total Cost = 150 square meters * Rp30,000.00/square meter
Total Cost = Rp4,500,000.00
Ta-da! The total cost to plant grass in the triangular garden is Rp4,500,000.00. This is the amount we would need to budget for the landscaping project. Pretty simple, right? From area calculation to calculating the total cost, we have completed our calculations.
Now, let's examine the options to identify the correct answer choice. We will compare our calculated total cost to the given choices to find the right answer. This final step confirms our understanding and ensures we select the correct solution.
Matching the Answer to the Given Options
Now that we have the final answer, let's go back and check the multiple-choice options, which were originally provided to us. Let's assume the provided options were:
A. Rp3,000,000.00 B. (This option was not fully provided) C. Rp4,000,000.00
Our calculated total cost is Rp4,500,000.00. However, since the correct option is not in the choices, let's look for the closest answer. We can see that the closest answer to our calculation is C. Rp4,000,000.00. Therefore, if we must choose from the original options, C would be the closest one.
Conclusion: Landscaping and Math are a Perfect Match
And there you have it, guys! We've successfully calculated the total cost of planting grass in our triangular garden. We started with the dimensions of the garden, calculated its area, and then figured out the total cost based on the cost per square meter of grass. It shows you how useful math can be in real-life situations, like planning a landscaping project. This problem isn't just about math; it's about seeing how math applies to real-world scenarios, making it more interesting and relevant. From here, you can see how important math is. So next time you see a beautiful lawn or garden, remember the math that made it possible. Keep practicing, and you'll be able to solve these types of problems in no time. Thanks for joining me, and keep exploring the amazing world of math!