A trapezoid has one base equal to twice its height, $x$, and the other base is three times as long as the height. Write the expression for the area of the trapezoid as a common fraction in terms of the height $x$.

Explanation:

Let x represent height of the trapezoid.

We have been given that a trapezoid has one base equal to twice its height, so one base of trapezoid would be .

We are also told that the other base is three times as long as the height, so other base of trapezoid would be .

Now, we will use area of trapezoid formula to write our required expression.

, where, a and b represent parallel bases of trapezoid and h represents height.

Upon substituting the expressions for bases of trapezoid in area formula, we will get:

Therefore, our required expression for the area of the trapezoid as a common fraction in terms of the height would .

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