Find the indicated measurement. Draw and label a diagram, and show your work Given: Trapezoid with bases 22 ft and 14 ft and an area of \( 108 \mathrm{ft}^{3} \) Find: height

To find the height of the trapezoid, we can use the area formula for a trapezoid, which is given by: \[ \text{Area} = \frac{(b_1 + b_2)}{2} \times h \] where \( b_1 \) and \( b_2 \) are the lengths of the bases, and \( h \) is the height. Given that the bases are 22 ft and 14 ft, and the area is 108 ft², we can substitute these values into the formula: \[ 108 = \frac{(22 + 14)}{2} \times h \] This simplifies to: \[ 108 = \frac{36}{2} \times h \] \[ 108 = 18h \] Now, divide both sides by 18 to solve for \( h \): \[ h = \frac{108}{18} = 6 \text{ ft} \] Now let’s visualize this! Picture a trapezoid with the longer base (22 ft) at the bottom and the shorter base (14 ft) at the top. The height drops straight down from one base to the other, creating right angles at each end. Label the top base as 14 ft, the bottom base as 22 ft, and the height as 6 ft. Voilà! You've found the height!