7.) The seat of a bench is in the shape of a trapezold with bases of 6 feet and 5 feet and a height of \( 1 \frac{1}{2} \) feet What is the area of the seat? \[ A=\frac{1}{2}\left(b_{1}+b_{2}\right) h \]

To find the area of the seat of the bench, which is in the shape of a trapezoid, we can use the formula for the area of a trapezoid: \[ A = \frac{1}{2} \times (b_1 + b_2) \times h \] Given: - \( b_1 = 6 \) feet (base 1) - \( b_2 = 5 \) feet (base 2) - \( h = 1 \frac{1}{2} \) feet (height) Substitute the given values into the formula: \[ A = \frac{1}{2} \times (6 + 5) \times 1 \frac{1}{2} \] Now, we can calculate the area of the seat of the bench. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}\left(6+5\right)\times 1.5\) - step1: Add the numbers: \(\frac{1}{2}\times 11\times 1.5\) - step2: Multiply the terms: \(\frac{11}{2}\times 1.5\) - step3: Convert the expressions: \(\frac{11}{2}\times \frac{3}{2}\) - step4: Multiply the fractions: \(\frac{11\times 3}{2\times 2}\) - step5: Multiply the terms: \(\frac{33}{2\times 2}\) - step6: Multiply the terms: \(\frac{33}{4}\) The area of the seat of the bench is \(8\frac{1}{4}\) square feet.