How do you convert area to perimeter? - Answers

Converting perimeter, the linear distance around the outside of a shape, to the area of the shape has no "general" formula. Each shape has its own characteristics, and we must apply different ways to find the area enclosed by a given perimeter for each shape. It is the geometry of the shape that will direct our efforts. Let's look at some shapes for a given perimeter and see what's up. If we have a square with a perimeter of 20, we know we have a shape with 4 equal sides which add up to 20. Our 20 divided by 4 is 5. That's 4 sides of length 5 (5 + 5 + 5 + 5 = 20), and the area equal to the square of a side, or 52, or 25 square units. What about a rectangle with a perimeter of 20? Is it a shape with a length of 6 and a width of 4, or it is a length of 8 and a width of 2? Both have the same perimeter, a perimeter of 20. But one has an area of 6 x 4 = 24 square units, and the other has an area of 8 x 2 = 16 square units. See the problem? Fasten your seatbelt. It gets worse. What if we have a circle with a perimeter of 20? The perimeter of a circle is called its circumference, and its equal to pi times the diameter, or pi times 2 times the radius (because a diameter is 2 radii). In the case of the circle, its area is pi times the square of the radius. If we do some math here, we'll find the area of the circle is 100 divided by pi. (We left out showing the work.) That makes the area of the circle about 31.85 square units. We've just converted the perimeter of 4 different geometric shapes into areas. And no two are alike. It wasn't too tough with the square, but we hit a snag with the rectangle. We needed more data. We were lucky with the circle. As shapes become more complex, we need "clues" to solve perimeter-to-area "conversions" for the shapes. There are rules and methods for discovering the area of a shape based on the perimeter and a little bit of other data. And we need bits of data in addition to just the perimeter of the shape, the primary one being the type of geometric figure itself. What if it was a kite? A rhombus or parallelogram? An ellipse? See how "complicated" it can get? As we pick our way through geometry, we start to gain some insight into how we can find out things about these shapes to define and measure them. Good luck picking up the tools to handle the job.