Question

In the trapezoid below, if CD = 15 m, PC = 10 m, and the area of the trapezoid = 185 m 2, find the length of side AB.

Answer 1

Explanation:

The area of a trapezoid is given by

`Area=(a+b)/(2)* h`

where a and b are base lengths and h is the height of the trapezoid.

Now in our case,

`\begin{gathered} a=CD=15 \\ b=AB \\ h=PC=10 \end{gathered}`

and the area is 185 m^2; therefore, our formula gives

`(15+AB)/(2)*10=185`

We just need to solve for AB.

Dividing both sides by 10 gives

`(15+AB)/(2)=18.5`

multiplying both sides by 2 gives

`\begin{gathered} 15+AB=18.5*2 \\ \Rightarrow15+AB=37 \end{gathered}`

subtracting 15 from both sides gives

`\begin{gathered} AB=37-15 \\ \boxed{AB=22.} \end{gathered}`

which is our answer!