What is the length in inches of the smaller base of a trapezoid with an area of 128 square inches, a height of 16 inches, and one base of 11 inches?

To determine the length of the smaller base of the trapezoid, we can use the formula for the area of a trapezoid:

[

\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h

]

where ( b_1 ) and ( b_2 ) are the lengths of the two bases, and ( h ) is the height. In this case, we know that the area is 128 square inches, the height is 16 inches, and one of the bases (let's say ( b_1 )) is 11 inches.

Plugging the known values into the formula gives us:

[

128 = \frac{1}{2} \times (11 + b_2) \times 16

]

To simplify, we can first multiply both sides by 2 to eliminate the fraction:

[

256 = (11 + b_2) \times 16

]

Next, divide both sides by 16:

[

16 = 11 + b_2

]

Now, we can solve for ( b_2 ):

[

b_2 = 16 -