Arthur's Tabletop Garden Calculating Area And Plant Capacity
Hey guys! Ever wondered how much space those lovely plants actually take up? Let's dive into a cool math problem about Arthur and his green companions. We're going to figure out the total area Arthur can cover on his table by arranging his potted plants in a neat rectangular pattern. Plus, we'll calculate how many pots he can squeeze into that space. Buckle up; it's math time, but the fun kind!
Decoding the Planting Pattern
Our main goal here is to understand how to calculate the total area Arthur can cover with his plants. We know he's arranging them in a rectangle that's 2 meters long and 1.5 meters wide. To kick things off, we need to figure out the total area of this rectangle. Remember, the area of a rectangle is simply its length multiplied by its width. So, in Arthur's case, we're looking at 2 meters * 1.5 meters.
But wait, there's more! Each of Arthur's plant pots occupies a little patch of land – 0.1 square meters, to be precise. This tidbit is crucial because it'll help us figure out how many pots can comfortably fit within our calculated area. Think of it like a puzzle where we're fitting these little 0.1 square meter pieces into a larger rectangular space. To solve it, we'll use some basic arithmetic, focusing on division and ensuring our units (square meters) play nicely together.
The key here is visualizing the problem. Imagine Arthur's tabletop as a grid, and each plant pot as a tile filling up that grid. By calculating the total area and knowing the area each pot takes up, we can figure out how many 'tiles' Arthur can place. It's a practical problem with a real-world application, showing us how math can help in everyday situations, like planning the perfect plant arrangement!
Calculating Total Coverage The Area of the Rectangle
Okay, let's get down to the nitty-gritty and calculate the total area Arthur's rectangular plant arrangement will cover. As we touched on earlier, the formula for the area of a rectangle is super straightforward: Area = Length * Width. In our scenario, Arthur's rectangle has a length of 2 meters and a width of 1.5 meters. So, we simply multiply these two numbers together: 2 meters * 1.5 meters. This calculation will give us the total area in square meters, which is the unit we use for measuring area. It's crucial to keep units consistent throughout the problem to avoid any confusion.
When we perform the multiplication, 2 * 1.5 equals 3. Therefore, the total area Arthur's plant arrangement will cover is 3 square meters. This is the overall space we have to work with, the canvas on which Arthur will paint his green masterpiece. Now that we know the total area, we're one step closer to figuring out how many plant pots can actually fit within this space. We've established our 'canvas' size, and next, we'll see how many 'tiles' (plant pots) we can place on it.
This step is all about laying the foundation. We've calculated the total available space, and this number, 3 square meters, is our anchor point. Everything else we calculate will relate back to this figure. It's a classic example of how geometry, the study of shapes and spaces, can help us solve practical problems. So, with our total area in hand, we're ready to move on to the next part of our puzzle: figuring out how many plants can call this 3 square meter space home.
Counting the Pots Dividing Area per Pot
Now comes the fun part where we figure out exactly how many plant pots Arthur can squeeze into his 3 square meter garden. We know that each pot occupies an area of 0.1 square meters. Think of it as each pot claiming its own little 0.1 square meter territory. So, the question becomes: how many 0.1 square meter territories can fit inside a 3 square meter space? This is a classic division problem!
To solve it, we simply divide the total area (3 square meters) by the area each pot occupies (0.1 square meters). The formula here is: Number of pots = Total area / Area per pot. Plugging in our numbers, we get: Number of pots = 3 square meters / 0.1 square meters. When we perform this division, we're essentially figuring out how many times 0.1 fits into 3. Remember, dividing by a decimal can sometimes seem tricky, but it's just like asking how many tenths are in three whole units.
The result of 3 / 0.1 is 30. This means Arthur can fit a grand total of 30 plant pots within his rectangular arrangement. That's a pretty impressive little garden! We've successfully used division to translate area measurements into a count of objects, showing how mathematical operations can help us quantify real-world scenarios. This calculation is the heart of our problem, answering the question of capacity: how many plants can this space accommodate?
Final Answer
So, let's wrap it all up and get to the final answer. Arthur can cover a total area of 3 square meters on his table by arranging his plant pots in a rectangle that's 2 meters long and 1.5 meters wide. And, with each pot occupying 0.1 square meters, he can fit a whopping 30 pots in that space! We've successfully navigated this mathematical puzzle, using both multiplication to calculate the total area and division to determine the number of pots.
This problem is a great example of how math concepts like area and division are relevant in everyday life. Whether you're arranging plants, planning a garden, or even figuring out how many tiles you need for a floor, these calculations come into play. By breaking down the problem into smaller steps – calculating the total area first, then dividing by the area per pot – we made it much easier to solve.
And there you have it, guys! We've unlocked Arthur's tabletop territory and discovered the power of math in planning the perfect plant display. Who knew numbers could be so green-thumbed friendly?
