Trapezoid Area Formula: Height Equals Sum of Bases with X-5 Difference

To express the area of the trapezoid in terms of $X$, we follow these steps:

• Step 1: Identify given measurements of the trapezoid.
  • Large base $= X$.
  • Small base $= X - 5$.
  • Height $= 2X - 5$.
• Step 2: Use the trapezoid area formula: $\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$
• Step 3: Substitute the values: $\text{Area} = \frac{1}{2} \times (X + (X - 5)) \times (2X - 5)$
• Step 4: Simplify the expression: $\text{Area} = \frac{1}{2} \times (2X - 5) \times (2X - 5)$ $\text{Area} = \frac{1}{2} \times (2X - 5)^2$ $\text{Area} = \frac{1}{2} \times (4X^2 - 20X + 25)$
• Step 5: Conclude with the expression for the area: $\text{Area} = \frac{1}{2}[4X^2 - 20X + 25]$

Therefore, the expression for the area of the trapezoid in terms of $X$ is $\frac{1}{2}[4X^2 - 20X + 25]$.