By Kat Black – Updated Aug 30, 2022
robertprzybysz/iStock/Getty Images
In geometry, variables appear whenever we need to determine a missing measurement from a given set of known values. Whether you’re working with perimeter, area, or volume, the process for finding a variable is consistent and systematic.
Choose the formula that directly relates the known quantities to the unknown. For example, the area of a triangle is calculated as A = ½ b h, where b is the base and h is the height.
Replace the variables in the formula with the measurements you’re given. If the area is 100 sq in and the base is 20 in, the equation becomes 100 = ½ (20 × h). Here, h is the variable we must solve for.
Apply the reverse of the order of operations (SADMEP) to move all other terms to the opposite side of the equation.
Whenever the equation calls for multiplication, divide; whenever it calls for subtraction, add; and so forth.
Continue the operations on both sides until the variable stands alone. Starting from 100 = ½ (20 × h), multiply both sides by 2 to remove the ½, yielding 200 = 20 h. Then divide both sides by 20 to find h = 10 in.
Ensure all measurements use the same unit. If the area is in square feet but a side length is in inches, convert the area to square inches before proceeding.
