How to Find the Height of a Trapezoid

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Because the height of the trapezoid does not usually lie along an edge of the shape, students have a challenge when it comes to finding the exact height. By learning the geometric equation that relates the trapezoid’s area to its bases and height, you can play some algebraic shuffling to directly calculate the height.

    Set up the equation for the area of a trapezoid. Write A=h(b1+b2)/2, where A represents the trapezoid’s area, b1 represents one of the base lengths, b2 represents the other base length and h represents the height.

    Rearrange the equation to get h alone. Multiply both sides of the equation by 2 to get. 2A=h(b1+b2). Divide both sides of the equation by the sum of the bases to get 2A/(b1+b2)=h. This equation gives the representation of h in terms of the other traits of the trapezoid.

    Plug in the values of the trapezoid into the equation for height. For example, if the bases are 4 and 12 and the trapezoid’s area is 128, plug them into the equation to reveal h=2*128/(4+12). Simplifying to a single number gives the height as 16.

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About the Author

Having obtained a Master of Science in psychology in East Asia, Damon Verial has been applying his knowledge to related topics since 2010. Having written professionally since 2001, he has been featured in financial publications such as SafeHaven and the McMillian Portfolio. He also runs a financial newsletter at Stock Barometer.

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