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