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)=(1)/(2)(x*24) \end{gathered}`

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

`x=√(25^2-24^2)=√(49)=7`

Then, the area of the trapezoid is,

`\Rightarrow A_(trapezoid)=A_(rectangle)+A_(triangle)=48*7+(1)/(2)(7*24)=336+84=420`

Thus, the answer is 420 ft^2.