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How to Find the Perimeter of a Trapezoid With a Missing Side

by Stephanie Ellen, Demand Media

    A trapezoid is a quadrilateral with two parallel sides. In geometry, you may be asked to find a missing side of a trapezoid, given the area and height. For example: a trapezoid has an area of 171 cm^2, a side of 10 cm and a height of 18 cm. How long is the missing side? Finding it takes some basic principles of geometry and a splash of algebra.

    Step 1

    Substitute the information given in the question to the formula for finding the area of a trapezoid (A=.5height (base1+base2)). 171=(.5)*18(10+base2).

    Step 2

    Multiply out .5 by 18: 171= 9(10+base 2).

    Step 3

    Use the distributive property to multiple out the equation: 171= 90+9(base 2).

    Step 4

    Use algebra to solve the remainder of the problem. Subtract 90 from both sides: 81=9(base2), then divide each side by 9. 9=base 2.

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    About the Author

    Stephanie Ellen teaches mathematics and statistics at the university and college level. She coauthored a statistics textbook published by Houghton-Mifflin. She has been writing professionally since 2008. Ellen holds a Bachelor of Science in health science from State University New York, a master's degree in math education from Jacksonville University and a Master of Arts in creative writing from National University.