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

Given a trapezoid whose height is equal to the sum of the two bases.

It is known that the difference between the large base and the small base is equal to 5. We will mark the large base with X

Express the area of the trapezoid using X

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 $\frac{1}{2}[4X^2 - 20X + 25]$.