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Shapes
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Areas
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Perimeters
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16
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16
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 |
16
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22
|
 |
16
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28
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16
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34
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Did you notice that the areas are all the same? This is because the shapes were all drawn using 4 purple bars. Each purple bar has an area of 4, and regardless of the shape these 4 purple bars always add up to 16.
Did you notice that the perimeters are all very different? Do you know why? The perimeter depends on how the bars overlap or how much of their edges touch. The perimeter is smallest when as many edges as possible touch each other. The perimeter is largest when the fewest edges touch each other.
Here are two shapes with a perimeter of 16:
Here are two shapes with a perimeter of 20:
As you can tell there are many different shapes that have the same perimeter so your shapes are probably different than the shapes we have drawn here.
Draw two different shapes; one that has an area of 15 and
another with an area of 28.
There are many different shapes that have an area of 15. Here are two creative examples and you probably drew a different shape which also has an area of 15.
Here are two different shapes that have an area of 28. Your answer may be different.
There are many different shapes that have an area of 15. Here are two creative examples and you probably drew a different shape which also has an area of 15.
Here are two different shapes that have an area of 28. Your answer may be different.
The shape with the smallest perimeter is as close to a square or rectangle as possible so that it has the most edges touching each other. The greater number of edges touching decreases the size of the perimeter. In this case we have drawn the rectangle shown below. It has a perimeter of 14.
To draw a shape with the largest perimeter we need to have the fewest possible edges touching each other. There are many different shapes that have the largest perimeter and the simplest one is a train as shown in the first drawing below. As you can see, the second drawing has the same number of edges touching each other and the same perimeter which is 26.
The perimeter of different shapes drawn with the same bars can vary a great deal. The area, however, is always the same, which is 12.
As we saw in the previous exercise, a square or a rectangle always has the smallest perimeter for the same area. Therefore, a square or rectangle will always give the largest area for the given perimeter. In this case, a square with all sides with a length of 7 has a perimeter of 28 and an area of 49.
