Question

find the area of the trapezoid. If the answer is not an integer, leave it in simplest radical form. The figure is not to scale.A= __ ft squared use radicals IF needed

Answer 1

The trapezoid can be divided into a rectangle and a right triangle, calculate the area of each one of the two figures as shown below

$\begin{gathered} A_{rectangle}=48x \\ A_{triangle}=\frac{1}{2}(x*24) \end{gathered}$

Where x is the missing side of the right triangle, find it using the Pythagorean theorem,

$x=\sqrt{25^2-24^2}=\sqrt{49}=7$

Then, the area of the trapezoid is,

$\Rightarrow A_{trapezoid}=A_{rectangle}+A_{triangle}=48*7+\frac{1}{2}(7*24)=336+84=420$

Thus, the answer is 420 ft^2.