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 given the bases and the area, we can use the formula for the area of a trapezoid: \[ A = \frac{1}{2} (b_1 + b_2) h \] where: - \( A \) is the area, - \( b_1 \) and \( b_2 \) are the lengths of the two bases, - \( h \) is the height. ### Step 1: Identify the known values From the problem, we have: - \( b_1 = 22 \, \text{ft} \) - \( b_2 = 14 \, \text{ft} \) - \( A = 108 \, \text{ft}^2 \) (Note: The area should be in square feet, not cubic feet) ### Step 2: Substitute the known values into the area formula We can rearrange the area formula to solve for height \( h \): \[ h = \frac{2A}{b_1 + b_2} \] Substituting the known values: \[ h = \frac{2 \times 108}{22 + 14} \] ### Step 3: Calculate the height Now, let's perform the calculations step by step. 1. Calculate the sum of the bases: \[ b_1 + b_2 = 22 + 14 = 36 \] 2. Calculate \( 2A \): \[ 2A = 2 \times 108 = 216 \] 3. Now substitute these values into the height formula: \[ h = \frac{216}{36} \] 4. Finally, calculate \( h \): \[ h = 6 \, \text{ft} \] ### Conclusion The height of the trapezoid is \( 6 \, \text{ft} \). ### Diagram Here is a simple representation of the trapezoid: ``` +-------------------+ / \ / \ +-----------------------+ 22 ft 14 ft ``` - The top base is \( 14 \, \text{ft} \). - The bottom base is \( 22 \, \text{ft} \). - The height \( h \) is \( 6 \, \text{ft} \).