Question

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 $x$.

Answer 1

Answer:

$\frac{5x^2}{2}$

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 $2x$.

We are also told that the other base is three times as long as the height, so other base of trapezoid would be $3x$.

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

$\text{Area of trapezoid}=\frac{a+b}{2}\cdot h$, 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:

$\text{Area of trapezoid}=\frac{2x+3x}{2}\cdot x$

$\text{Area of trapezoid}=\frac{5x}{2}\cdot x$

$\text{Area of trapezoid}=\frac{5x^2}{2}$

Therefore, our required expression for the area of the trapezoid as a common fraction in terms of the height would $\frac{5x^2}{2}$.