Step-by-Step Solutions for Trapezoid Problems

Finding the area of a trapezoid, a four-sided polygon with two parallel sides, is one of the most basic math problems involving trapezoids. You are often given the height of the trapezoid and length of each of its two parallel sides (the trapezoid's bases) and asked to find the area. The solution requires you perform just three simple arithmetic operations: addition, multiplication and division. Other trapezoid problems are often variations of this problem. One typical trapezoid problem requires you find the height of the trapezoid given the area and the length of the bases.

Things You'll Need

  • Calculator
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Instructions

  1. Finding Area

    • 1

      Measure the length of each of the trapezoid's bases. Or you may be given this information. Add the result together to obtain the sum of the length of the bases.

    • 2

      Measure the distance of a vertical line (the height of trapezoid) that extends between the two base lines on the trapezoid. Again, you may be given this information in the problem.

    • 3

      Multiply the sum of the trapezoid bases by the height of the trapezoid. Divide the result by 2 to obtain the trapezoid's area.

    • 4

      Verify that area for a trapezoid that has one base with a length of 2, another base with a length of 3 and a height with a length of 5 is 12.5. Add 2 plus 3 to obtain 5 and multiply this result by the height to obtain 25. Then divide the result by 2 to obtain the correct result: 12.5 square units.

    • 5

      Use the trapezoid area calculator at the "Trapezoid Area Calculator" link in Resources to check your math and procedures.

    Find the Height

    • 6

      Write down the variables given for the trapezoid problem. Suppose you're given a trapezoid area of 3, a lower base length of 2 and an upper base length of 1 for this problem, in which you must solve for height.

    • 7

      Substitute these variables into the trapezoid area formula:

      Area = height * (base1 + base2)/2

      So you would obtain 3 = height*(1 + 2)/2. Multiply both sides of the equation by 2 to obtain 6 = 3*height. Divide both sides of the equation by 3 to obtain a height of 2.

    • 8

      Verify that 2 is the answer by substituting the height calculated and the variables given back into the area formula. So area = (2)*(1 + 2)/2. Simplify the expression to A = (1 + 2) by canceling the twos. Add the result to obtain an area of 3.

      You can conclude that 2 is the correct answer for the height because the area given for the original problem was also 3.

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