if one of the bounding functions is linear instead of quadratic. Surface area of 3-dimensional figures Cone: , where r is the radius of the circular base, and h is the height. That can also be rewritten as or where r is the radius and l is the slant height of the cone. is the base area while is the lateral surface area of the cone. Cube: , where s is the length of an edge. Cylinder: , where r is the radius of a base and h is the height. The can also be rewritten as , where d is the diameter. Prism: , where B is the area of a base, P is the perimeter of a base, and h is the height of the prism. pyramid: , where B is the area of the base, P is the perimeter of the base, and L is the length of the slant. Rectangular prism: , where is the length, w is the width, and h is the height. General formula for surface area The general formula for the surface area of the graph of a continuously differentiable function where and is a region in the xy-plane with the smooth boundary: An even more general formula for the area of the graph of a parametric surface in the vector form where is a continuously differentiable vector function of is: List of formulas The above calculations show how to find the areas of many common shapes. The areas of irregular (and thus arbitrary) polygons can be calculated using the "Surveyor's formula" (shoelace formula). Relation of area to perimeter The isoperimetric inequality states that, for a closed curve of length L (so the region it encloses has perimeter L) and for area A of the region that it encloses, and equality holds if and only if the curve is a circle. Thus a circle has the largest area of any closed figure with a given perimeter. At the other extreme, a figure with given perimeter L could have an arbitrarily small area, as illustrated by a rhombus that is "tipped over" arbitrarily far so that two of its angles are arbitrarily close to 0° and the other two are arbitrarily close to 180°. For a circle, the ratio of the area to the circumference (the term for the perimeter of a circle) equals half the radius r. This can be seen from