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What is the formula for finding an equable shape?
For any shape, there is a similar equable shape: if a shape S has perimeter p and area A, then scaling S by a factor of p/A leads to an equable shape. Alternatively, one may find equable shapes by setting up and solving an equation in which the area equals the perimeter. In the case of the square, for instance, this equation is
What is a two-dimensional equable shape?
A two-dimensional equable shape (or perfect shape) is one whose area is numerically equal to its perimeter. For example, a right angled triangle with sides 5, 12 and 13 has area and perimeter both have a unitless numerical value of 30.
What is an example of an equable shape?
However its common use as GCSE coursework has led to its being an accepted concept. For any shape, there is a similar equable shape: if a shape S has perimeter p and area A, then scaling S by a factor of p/A leads to an equable shape.
When does a shape become an equable shape?
In three dimensions, a shape is equable when its surface area is numerically equal to its volume . As with equable shapes in two dimensions, you may find an equable solid, in which the volume is numerically equal to the surface area, by scaling any solid by an appropriate factor.
Last Update: Oct 2021
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