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28 June, 05:48

The area of a trapezoid is 18 square meters. One base is 3 meters long and the other is 6 meters long. Find the height of the trapezoid. Step 2 of 3 : Without substitution, solve the formula chosen in the previous step for the unknown variable in terms of the known variable (s).

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  1. 28 June, 09:14
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    height = 4 meters

    h = 2A / (a + b)

    Step-by-step explanation:

    Let A represent the area of the trapezoid, h, the height a, the length of one base and b, the length of the other base

    Area of a trapezoid, A = (a + b) * h / 2

    Now let's slot in the given values

    A = 18 sq meters

    a = 3 meters

    b = 6 meters

    we have;

    18 = (3 + 6) * h / 2

    18 = 9 * h / 2

    Cross multiply

    18*2 = 9h

    36 = 9h

    divide both sides by the coefficient of h (9)

    4 = h

    therefore, h = 4 meters

    To solve for h without substituting

    From A = (a + b) * h / 2

    cross multiply

    2*A = (a + b) * h

    divide both sides by (a + b)

    2A / (a + b) = h

    therefore,

    h = 2A / (a + b)
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