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anonymous

  • one year ago

The area of a trapezoid is 144 ft 2. If the height is 8 feet and one of the bases is 12 feet, what is the length of the other base? 7.2 ft 14.4 ft 24 ft 16 ft

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  1. calculusxy
    • one year ago
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    The formula for finding the area of a trapezoid is: \[\frac{ 1 }{ 2 }(b_1 + b_2)\times h\]

  2. calculusxy
    • one year ago
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    There are some information that are already aware of and so using those information should help you find one of the base. Information that you already know: Area = 144ft^2 Height = 8 feet One of the bases (b_1) = 12 feet

  3. calculusxy
    • one year ago
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    Now what you can do is plug those information into the formula: \[\frac{ 1 }{ 2 }(12ft+b_1)\times 8ft = 144ft^2\]

  4. calculusxy
    • one year ago
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    Simplify this and, first, you need to distribute 1/2 to 12ft and let's keep b_1 as simply "b". \[\frac{ 1 }{ 2 }(12 ft + b) = \frac{ 1 }{ 2 }(12ft) + \frac{ 1 }{ 2 }(b) = 6 + \frac{ 1 }{ 2 }b\] Let's insert this with the remaining formula: \[6 + \frac{ 1 }{ 2 }b \times 8ft = 144ft^2\]

  5. calculusxy
    • one year ago
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    \[(12ft + b) \times 8ft = 144ft^2 => 4b = 132 => b = 33\] but if i do the same thing, but with 8b, then i get the value of b as 16.5 @Nnesha

  6. Nnesha
    • one year ago
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    it's not 8 remember we divided by 2 \[\rm \frac{ 1 }{ \cancel{2} }(12+b)\cancel{8}=4(12+b)\]

  7. calculusxy
    • one year ago
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    48 + 4b = 144 b = 24 right ? @Nnesha

  8. Nnesha
    • one year ago
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    yes you can distribute by 4 but you don't have to i wouldn't do that \[\frac{ 4(12+b) }{ 4}=\frac{ 144 }{ 4 }\] and yes tha'ts right

  9. calculusxy
    • one year ago
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    Thank you :)

  10. Nnesha
    • one year ago
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    :)

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