[1] For example, a right angled triangle with sides 5, 12 and 13 has area and perimeter both with a unitless numerical value of 30.
Alternatively, one may find equable shapes by setting up and solving an equation in which the area equals the perimeter.
Every tangential polygon may be triangulated by drawing edges from the circle's center to the polygon's vertices, forming a collection of triangles that all have height equal to the circle's radius; it follows from this decomposition that the total area of a tangential polygon equals half the perimeter times the radius.
[5][6] As W. A. Whitworth and D. Biddle proved in 1904, there are exactly three solutions, beyond the right triangles already listed, with sides (6,25,29), (7,15,20), and (9,10,17).
[9] In three dimensions, a shape is equable when its surface area is numerically equal to its volume.