How do you solve for the base ‘m’ in the area formula of a trapezoid given the altitude ‘k’ and the other base ‘n’?

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The area of a trapezoid can be calculated using the formula:

Area = (1/2) * (m + n) * k

In this formula, ‘m’ and ‘n’ are the lengths of the two bases of the trapezoid, and ‘k’ is the height (or altitude). To solve for ‘m’, you’ll need to rearrange the formula.

Here are the steps to isolate ‘m’:

  1. Start with the area formula:
    2. Area = (1/2) * (m + n) * k
  2. Multiply both sides by 2 to eliminate the fraction:
    3. 2 * Area = (m + n) * k
  3. Next, divide by ‘k’ to isolate the term with ‘m’:
    4. (2 * Area) / k = m + n
  4. Now, subtract ‘n’ from both sides to solve for ‘m’:
    5. m = (2 * Area) / k - n

Thus, the formula to find ‘m’, the length of one base of the trapezoid, is:

m = (2 * Area) / k - n

By following these steps, you should be able to calculate the length of base ‘m’ using the area of the trapezoid, the height, and the length of the other base ‘n’. Make sure to use consistent units throughout your calculations for accuracy!

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