Calculate Trapezoid Area: Finding Area with Sides 2X and 3Y

To determine the area of the trapezoid, we will use the formula for the area of a trapezoid:

$A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

From the problem, the two bases are $2X$ and $3Y$. The height is $X$.

Substituting into the formula, we have:

$A = \frac{1}{2} \times (2X + 3Y) \times X$

Simplifying the expression inside the parenthesis gives:

$A = \frac{1}{2} \times (2X + 3Y) \times X = \frac{1}{2} \times (2X \times X + 3Y \times X)$

Distributing $X$ through the terms inside the parenthesis gives:

$A = \frac{1}{2} \times (2X^2 + 3XY)$

Continuing the simplification:

$A = \frac{1}{2} \times 2X^2 + \frac{1}{2} \times 3XY$

Which simplifies to:

$A = X^2 + 1.5XY$

Therefore, the area of the trapezoid is $X^2 + 1.5XY$ cm².

Through comparison, this expression matches the given choice: $x^2+1.5xy$ cm², which corresponds to choice $3$.

Thus, the correct area of the trapezoid is $x^2 + 1.5xy$ cm².