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Consider a square with sides of length x cm whose area is x2 cm and perimeter is 4x cm.
Next consider a rectangle with sides of 2x cm and x/2 cm. It area is 2x*x/2 = x2, the same as for the square. But its perimeter is 2*(2x+x/2) = 5x > perimeter of the square.
Perimeter of 3x * x/3 = 62/3x cm.
Perimeter of 100x * x/100 = 200.02x cm
Perimeter of 1000000x * x/1000000 = 2000000.000002x cm.
As you can see, it is possible to increase the perimeter without limit.
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How do you figure out the area if you know the perimeter?
You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.
What is the smallest figure with a perimeter of 20 but the smallest possible area?
A 9 x 1 rectangle has a perimeter of 20 and an area of 9; A 9.5 x 0.5 rectangle has the same perimeter but an area of 4.75; You can go a long way along this road...
Can you keep the perimeter the same and make the area smaller or larger?
Yes and no. You can make the area narrower or wider, but you can't actually change it.
Does a shape with a smaller perimeter always have a smaller area?
No, a shape with a smaller perimeter does not always have a smaller area. The relationship between perimeter and area depends on the specific shape in question. For example, a square with a perimeter of 12 units will have a larger area than a rectangle with the same perimeter. The distribution of perimeter and area varies based on the shape's dimensions and proportions.
If same area in a rectangle does that mean same perimeter?
No. For example, a 4x1 rectangle will have an area of 4 and a perimeter of 10. A 2x2 rectangle will have the same area of 4, but a perimeter of 8.
