We plan to add a fountain to our garden with the given dimensions. Let's copy the diagram with the garden and place the fountain inside it. We will place the garden exactly in the middle to retain symmetry. If we rotate the fountain, notice that we can place it sideways inside the garden. Let's label the given sides.
We want to find the area of the garden after we add a fountain to it. We can find it by two different methods. First, we will split the garden into 8 smaller rectangles of three different sizes. If we find the area of each of those rectangles, we can add them all together to find the total area of the garden.
Alternatively, we could notice that the fountain is also a rectangle shape and fits inside the garden. If we find the area of the fountain, we can subtract that from the area of the entire garden space. This would give us the area of the remaining garden.
Let's use the second method to find the area since we already have the dimensions of the fountain. We will find the area of the fountain, then subtract it from the area of the entire garden space. Recall that the area of a rectangle is the product of its width and its length. Let's write an expression to find the area of the remaining garden space.
Area=6 34* 9 16 - 3 13* 5 14
Before we evaluate this expression let's rewrite each mixed number as an improper fraction.
We found the areas of both the fountain and the entire garden space! Now we want to subtract the fractions to find the area of the remaining garden space. Before we can do that, we will rewrite the fractions so they have a common denominator. Let's do it!
We found that the area of the garden after we add a fountain is 44 38 square feet.
Extra
Smaller Rectangles Method
Let's find the area with the first method we described and see if the answers are the same. We can start by labeling the length of the Type 1 rectangles as l and the width as w.
We can see that the length of two Type 1 rectangles and the length of one Type 3 rectangle is equal to the length of the whole garden. Let's use this to write an equation and solve it for l.
Next, we can see from the diagram that the width of two type 1 rectangles and the width of a rectangle of type 2 is equal to the width of the whole garden. With that in mind, we can make an equation and solve it for w.
Next, notice that the length of a Type 1 rectangle is the same as the length of a Type 2 rectangle. The width of a Type 2 rectangle is 5 14 feet. With this in mind, we can find the area of a Type 2 rectangle.
Now, notice that the width of a Type 1 rectangle is the same as the width of a Type 3 rectangle. The length of a Type 3 rectangle is 3 13 feet. With this in mind, we can find the area of a Type 3 rectangle.
Finally, notice that there are four Type 1 rectangles and two of each Type 2 and 3 rectangles. Let's use multiplication to write an expression that will sum up all of these areas.
This is the same as our original answer, so we can be sure that we are correct. Notice that this method was more complex and took more time. Try to always think about ways to make the necessary calculations easier and faster by finding other methods to solve problems!
