1. Formulas for Lengths, Areas and Volumes

2. One-dimensional Measurement
Let’s consider the following formulas for calculating the lengths of figures.
Perimeter of a rectangle = 2(a + b)
The lengths in the figures are sums of the lengths (or multiples of the lengths) of some line segments.
We say that the measurement of length is a linear measurement, i.e. one-dimensional measurement.

3. Two-dimensional Measurement
Let’s consider the following formulas for calculating the areas of figures.
Area of a square = a2
Area of a parallelogram = ah
Total surface area of a cuboid = 2(ab + bc + ac)

4. The areas of the figures are the products of two lengths (or sum of the products of two lengths).
We say that the measurement of area is a quadratic measurement, i.e. two-dimensional measurement.

5. Three-dimensional Measurement
Let’s consider the following formulas for calculating the volumes of solids. h r 2 3 1 p
Volume of a circular cone = 3 4 r p
Volume of a sphere =
The volumes of the solids are the products of three lengths (or sum of the products of three lengths).
We say that the measurement of volume is a cubic measurement, i.e. three-dimensional measurement.

6. Let’s try to determine the dimensions of the following measurements.
 It includes the product of two lengths (i.e. r 2). r
Dimension = _________ 2
(b)
 It includes the product of three lengths (i.e. r 2h).
Dimension = _________ 3

7. (c) 4(a + b + c) Dimension = _________ 1 (d) Dimension = _________ 2
 It includes the sum of lengths.
Dimension = _________ 1
(d) l
 It includes the product of two lengths (i.e. rl ).
Dimension = _________ 2