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

Video Solution

Solution Steps

00:00 Express the area of the trapezoid using X

00:03 Use the formula for calculating the area of a trapezoid

00:07 (sum of bases) times height divided by 2

00:21 Let's take the fraction out of the parentheses

00:36 The same factor multiplied by itself is actually squared

00:40 Use the shortened multiplication formulas to expand the parentheses

00:49 Calculate the squares and products

01:01 And this is the solution to the question

Step-by-Step Solution

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