Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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:
\[6 + \frac{ 1 }{ 2 }b \times 8ft = 144ft^2\]

Answer 5

\[(12ft + b) \times 8ft = 144ft^2 => 4b = 132 => b = 33\]

but if i do the same thing, but with 8b, then i get the value of b as 16.5

@Nnesha

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Thank you :)

Answer 10

:)