(d) Once these conversions are completed, we now have the correct units, feet over
seconds. All that is left is to perform the math calculations. On the numerator side, multiply 5280 times
1 times 1. On the denominator side, multiply 60 times 60. The resulting solution (5,280 over 3,600)
equals 1.47 feet per second. Thus, through inferential mathematics, we can conclude that for every one-
mile per hour, distance traveled in feet per second equals 1.47.
d. Area. Area is the unit of measurement defined inside a figure. For different types of figures,
each has their own equation to figure out the area of that object. Area is always measured in square
units. For instance, we may measure area in square feet, square inches, or square miles.
(1) The area for squares and rectangles is very easy to determine. Just multiply the length of
two adjacent sides to determine the area inside the figure. For squares (which have all equal sides), just
multiply the length of one side twice to determine the area.
(2) Determining the area of circles is more difficult since it involves rounded area
Mathematicians in the past came up with a unit of measurement to figure the area of a circle, which they
labeled or pi. Pi is the ratio of the circumference of a circle to its radius. As you all know, pi is equal
to approximately 3.14, which means that for any given circle, its circumference will always be 3.14
times greater than its radius.
(3) Computing the area for a circle can be performed in one of two ways. The first way is to
take the radius and square it multiplying the product by pi (use 3.14 if you don't have a button on your
calculator). The second way is to multiply pi times the diameter squared (D) over four, or 0.785 times
the diameter squared. Make sure that the units agree (both in feet or both in inches, etc.).
(4) Example. Although determining the area for a rectangle and square is fairly straight
forward, many find determining the area of a circle to be more demanding. To illustrate, we will
determine the area of a circle in two different ways. For our example, we want to find the area of a
circle, in square inches, that have a diameter of two feet.
(a) After the calculation: Multiply the radius (one-foot) squared by 3.14. The area is
3.14 ft . To convert this to square inches, multiply by the number of square inches in one foot (12 x 12
= 144). Take 144 and multiply it by the answer (3.14 feet squared) and the final answer is 452.16 square
(b) Before the calculation: Convert the radius from feet to inches (1 foot = 12 inches).
Multiply the radius squared (144) by pi (3.14) and the answer is 452.16 square inches.
e. Solving for Unknown Variables. The last major section we must discuss is solving for unknown
variables. When given an equation with multiple variables and all other variables are known, the
equation can always be solved for the unknown variable. When solving for an unknown variable,
always delete all other variables from that side of the equation to separate the unknown variable. The
important thing to remember when solving for an unknown variable is that when deleting other variables
from one side of the equation, you must perform the opposite calculation to remove that variable.
Before solving for unknown variables, it is important to understand the hierarchies of mathematics to
correctly solve equations.
The correct hierarchies are as follows:
Perform all functions within parentheses first.