If a trapezoid has an area of 112 square centimeters, a height of 7 centimeters, and one base measuring 18 centimeters, what is the length of the other base?

To determine the length of the other base of the trapezoid, we utilize 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 the area of the trapezoid is 112 square centimeters, the height ( h ) is 7 centimeters, and one of the bases ( b_1 ) is 18 centimeters. We want to find the unknown base ( b_2 ).

Plugging in the known values into the area formula:

[

112 = \frac{1}{2} \times (18 + b_2) \times 7

]

To simplify this equation, first multiply both sides by 2 to eliminate the fraction:

[

224 = (18 + b_2) \times 7

]

Next, divide both sides by 7:

[

32 = 18 + b_2

]

Now, solve for ( b