Questions: The area of the trapezoid shown below is 20 square feet, the height is 5 feet, and the length of one base is 2 feet. What is b, the length of the other base, in feet?

Solution Steps

To find the length of the other base $b$ of the trapezoid, we can use the formula for the area of a trapezoid:

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

Given the area, height, and one base, we can rearrange the formula to solve for the other base.

We are given the area of the trapezoid as $20$ square feet, the height as $5$ feet, and one base ($\text{Base}_1$) as $2$ feet. We need to find the length of the other base ($b$).

The formula for the area of a trapezoid is:

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

Substituting the known values into the formula:

$$20 = \frac{1}{2} \times (2 + b) \times 5$$

First, simplify the equation:

$$20 = \frac{1}{2} \times (2 + b) \times 5$$

Multiply both sides by 2 to eliminate the fraction:

$$40 = (2 + b) \times 5$$

Divide both sides by 5:

$$8 = 2 + b$$

Subtract 2 from both sides to solve for $b$:

$$b = 6$$

Final Answer