TenMarks teaches you how the effect of changing dimensions on area.
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Learn About Area Changing Dimensions Change the figure. So in this problem, it states that a township wants to increase the size of its main park. The park is a rectangle that measure 125 x 80 feet. If the town buys and adjacent park that is exactly the same size and shape, how will this change the size of the park. So before we begin, let’s review about the area of a figure. So when we’re talking about the area of a figure, the area of a figure is a measure of the size of the region enclosed by a figure. So the area of a figure is the measure of the size of the region enclosed by a figure. Now, the perimeter on the other hand is the distance around the outside of a closed figure. Now, getting back to our problem, we need to find out how will this size, the change of size of the park if we add by the adjacent park with the same size and shape as the regular park. So to solve this, our first step in what we need to do is that we need to draw a diagram of the park. So we need to draw a diagram. So the original park is a rectangle that measures 125 feet x 80 feet. So I’m going to draw a diagram of the park to the best of my artistic ability. So here is my park and it’s 125 ft x 80 ft. And remember that with a rectangle, your opposite sides are of the same lengths. Alright, so our next step, step two then is to draw the diagram of the combined area. So now, we’re going to draw a diagram of the combined area. So how we are going to do this is that we know that the adjacent park is exactly the same measure as the township park. So it’s the same size and the same shape. So the length of the new park will be double the original length. So the width of the park will remain the same. So if we’re putting the park—so if we have our original park here, that’s 125 feet, and then we buy the adjacent park, so we’re doubling the length. But the width of the park stays the same but we doubled the original length. So the length of the new park will equal—we’ll put the length of the new park as L—will equal 125 for the original plus another 125 for the adjacent park, and this will be feet. So if I add these together, I get 250 ft. Now, the width of the new park which is W is going to remain the same. It’s going to be 80 ft. Because remember, we said that the width doesn’t change when we add the adjacent park. So this total shape here is the new park. So this is the area of the new park. So the parks are now adjoined by this dotted line. So this is how the parks are adjoined. So our next step is that after we have drawn our diagram and combined the areas, we now have to find the area of the new park. So to find the area of the original park, so we’re going to put the area of the original park, is going to be the length x width. So the length of the original park was 125 ft and the width was 80 ft. So that means that the area of the original park, I’ll just label this here, is going to be 10,000 ft2 and then the area of the new park is going to be the same thing, the length x the width where our length now is 250 ft and our width is 80, and when I multiply that, I get 20,000 ft2. So the area is increased two times, 2 x 10,000 is 20,000. Remember that when you have two similar figures joined together, the area of the new figure is doubled. So to get back to our problem, how will this change the size of the park? Well, it’s going to double the size of the park and we know that it’s going to double the size because we know that it increased it two times from 10,000 to 20,000. Let’s move on to our next problem. So here, we need to find the area and perimeter of the figure that would be formed at the dimensions of the figure given below or doubled. Alright, our original figure is a rectangle and it measures 5 ft x 5.5 ft. So to solve this, our first step is to find the area of the original rectangle. So the area of the original rectangle is going to equal the length x width. So the length of this rectangle is 5 and the width of the rectangle is 5.5