Mathematics
Grade9
Easy

Question

Find the area of the following trapezoid:

  1. 48 square root of 91 m squared
  2. 48 square root of 81 space straight m squared
  3. 52 square root of 91 m squared
  4. 52 square root of 101 m squared

The correct answer is: 48 square root of 91 m squared


    The formula for the area of a trapezoid is:
    A equals 1 half open parentheses b subscript 1 plus b subscript 2 close parentheses left parenthesis h right parenthesis
    where b1 is the length of one base, b2 is the length of another base, and h is the length of the height.
    Use the Pythagorean Theorem to find the height of the trapezoid:
    straight A squared plus straight B squared minus straight C squared
6 straight m squared plus straight B squared equals 20 straight m squared
straight B equals 2 square root of 91 straight m
    Plugging in our values, we get:
    A equals 1 half left parenthesis 18 m plus 30 m right parenthesis left parenthesis 2 square root of 91 m right parenthesis equals 48 square root of 91 m squared

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