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?

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?

• A. 10 centimeters
• B. 14 centimeters
• C. 12 centimeters
• D. 16 centimeters

Answer: (B)

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

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