volume_mute

Trapezoid

publish date: 2024/07/11 05:33:00 UTC

The formula for the area of a trapezoid is \(A = \frac12 h(a + b)\), where A is the area, h is the height, and a and b are the lengths of its bases.  Find A when \(h = 1\frac23\)in., \(a =2\frac12\) in., and \(b = 5\frac12\) in.

volume_mute

Correct Answer

$6\frac23$

Explanation

In the formula, we will replace the letter h with \(1\frac23\), the letter a with \(2\frac12\), and the letter b with \(5\frac12\).  Then we can use the order of operations rule to find the value of the expression on the right side of the = symbol.

  • This is the formula for the area of a trapezoid
    • \(A = \frac12h(a +b)\)
  • Replace h, a, and b with the given values
    • =\(\frac12 \left(1\frac23\right)\left(2\frac12 + 5\frac12 \right)\)
  • Do the addition within the parentheses: \(2\frac12 + 5\frac12 = 8\)
    • = \(\frac12 \left(1\frac23\right) (8)\)
  • To prepare to multiply fractions, write \(1\frac23\) as an improper fraction and 8 as \(\frac81\).
    • = \(\frac12 \left(\frac53\right)\left(\frac81\right)\)
  • Multiply the numerators.  Multiply the denominators.
    • = \(\frac{1 \cdot 5 \cdot 8}{2 \cdot 3 \cdot 1}\)
  • To simplify, factor 8 as 2 • 4.  Then remove the common factor of 2 from the numerator and denominator.
    • = \(\require{cancel} \frac{1 \cdot 5 \cdot \cancel{2}^1 \cdot 4}{\cancel{2}_1 \cdot 3 \cdot 1}\)
  • Multiply the remaining factors in the numerator.  Multiply the remaining factors in the denominator.
    • =\(\frac{20}{3}\)
  • Write the improper fraction \(\frac{20}{3}\) as a mixed number by dividing 20 by 3.
    • =\(6\frac23\)

The area of the trapezoid is \(6\frac23\) in.2

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