find the area of the trapezoid. if the answer is not an integer, leave it in simplest radical form. the…

Explanation:

Step1: Find the length of the base - extension

Use the Pythagorean theorem in the right - triangle on the right - hand side of the trapezoid. Let the base - extension be $x$. We know that in a right - triangle with hypotenuse $c = 17$ ft and height $a = 8$ ft, by the Pythagorean theorem $c^{2}=a^{2}+x^{2}$. So $x=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$ ft.

Step2: Identify the lengths of the bases and height of the trapezoid

The lengths of the bases of the trapezoid are $b_1$ and $b_2$, and the height is $h$. The shorter base $b_1$ (the vertical side of the non - rectangular part) is $8$ ft, the longer base $b_2=8 + 16=24$ ft, and the height $h = 15$ ft.

Step3: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$. Substitute $b_1 = 8$ ft, $b_2=24$ ft, and $h = 15$ ft into the formula. $A=\frac{(8 + 24)\times15}{2}=\frac{32\times15}{2}=240$ ft².

Answer:

$240$