Geometry

Package: GEOMETRY_PACKAGE. Registered by createEngine(); for a slimmer engine, register it explicitly (see choosing packages).

Work out the size of a shape from its measurements: the area it covers, the perimeter around its edge, the volume it holds, or its surface area. Name the measure, the shape, and the shape’s dimensions, and the formula is applied for you, no need to remember whether it was πr² or 2πr.

Flat shapes

area of circle radius 5 // 78.54
circumference of circle radius 5 // 31.42
area of square side 4 // 16
perimeter of square side 4 // 16
area of triangle base 3, height 4 // 6

A shape with two dimensions takes them as a pair, separated by a comma:

area of rectangle width 4, height 6 // 24
perimeter of rectangle width 4, height 6 // 20

The comma matters. Without it, 4 height reads as a number times a value called height (the ordinary “4x means 4 times x” rule), so the comma is what keeps the two measurements apart. It also means the dimension words (width, height, radius, …) stay ordinary words you can still use as names elsewhere.

Solid shapes

volume of sphere radius 3 // 113.10
surface area of sphere radius 3 // 113.10
volume of cube side 2 // 8
volume of cylinder radius 2, height 5 // 62.83
volume of cone radius 2, height 6 // 25.13

The shapes and their dimensions

• circle: radius (area, perimeter / circumference)
• square: side (area, perimeter)
• rectangle: width, height (area, perimeter)
• triangle: base, height (area)
• sphere: radius (volume, surface area)
• cube: side (volume, surface area)
• cylinder: radius, height (volume, surface area)
• cone: radius, height (volume)

Dimensions are plain numbers here (this does not yet carry units through to a squared or cubed result). A measure a shape does not define, or a missing dimension, is reported as an error naming what it needed rather than a wrong number.