How to Find the Value of a Variable in Geometry

You can use a formula to figure out values of variables in geometric figures.
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Variables, or unknown values, appear in numerous types of equations from simple algebra problems to complex calculus problems. In geometry, variables often appear in problems related to perimeter, area and volume. Typical problems provide you with some precise measurements and ask you to find out an unknown measurement, or variable.

    Determine which formula you need. For example, if you're working with the area of a triangle, you need to know that area equals one half the base times the height, or A=1/2bh.

    Plug the known values into the formula. Using the area of the triangle example, assume you know that the area is 100 square inches and the base is 20 inches. When you plug these values into the formula, you get 100=1/2 (20h). The height of the triangle is the variable.

    Use the order of operations in reverse to isolate the variable on one side of the equation. The order of operations is PEMDAS -- parentheses, exponents, multiplication, division, addition and subtraction. When solving for a variable, use the order in reverse -- SADMEP.

    Perform the opposite operation to what is called for in the equation. If the equation requires you to multiply, you will divide. If the equation calls for subtraction, you will add.

    Repeat the same operation on both sides of the equation. In the area of the triangle example, you arrived at the formula 100=1/2 (20h). You want to get the “h” by itself on one side of the equation. Multiply both sides of the equation by 2 to counteract the effect of the “1/2.” You then have 200=20h. Divide both sides of the equation by 20 to isolate the “h.” You find out that h=10.


    • Be sure all measurements use the same unit of measurement. If the problem gives an area in square feet and the length of side in inches, you will need to convert the feet to inches before solving the equation.

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