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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.

In the trapezoid below, if CD = 15 m, PC = 10 m, and the area of the trapezoid = 185 m-example-1
User Jason Sims
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1 Answer

6 votes

ANswer:

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!

User Ajmccall
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