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

ANswer:

Explanation:

The area of a trapezoid is given by

$Area=\frac{a+b}{2}\times h$

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

$\frac{15+AB}{2}\times10=185$

We just need to solve for AB.

Dividing both sides by 10 gives

$\frac{15+AB}{2}=18.5$

multiplying both sides by 2 gives

$\begin{gathered} 15+AB=18.5\times2 \\ \Rightarrow15+AB=37 \end{gathered}$

subtracting 15 from both sides gives

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

which is our answer!