## 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

1. calculusxy

The formula for finding the area of a trapezoid is: $\frac{ 1 }{ 2 }(b_1 + b_2)\times h$

2. calculusxy

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

Now what you can do is plug those information into the formula: $\frac{ 1 }{ 2 }(12ft+b_1)\times 8ft = 144ft^2$

4. calculusxy

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

$(12ft + b) \times 8ft = 144ft^2 => 4b = 132 => b = 33$ but if i do the same thing, but with 8b, then i get the value of b as 16.5 @Nnesha

6. Nnesha

it's not 8 remember we divided by 2 $\rm \frac{ 1 }{ \cancel{2} }(12+b)\cancel{8}=4(12+b)$

7. calculusxy

48 + 4b = 144 b = 24 right ? @Nnesha

8. Nnesha

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

Thank you :)

10. Nnesha

:)