To find the length of the second base of a trapezoid when we are given the area, the height, and the length of one of the bases, we can use the area formula for a trapezoid. The formula is:
\[ A = \frac{1}{2} \times h \times (b_1 + b_2) \]
where:
- \( A \) is the area of the trapezoid
- \( h \) is the height of the trapezoid
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel bases of the trapezoid
Given:
- The area of the trapezoid \( A = 126 \) square feet
- The height of the trapezoid \( h = 9 \) feet
- The length of one of the bases \( b_1 = 13 \) feet
We need to find the length of the second base \( b_2 \).
Let's follow these steps to solve for \( b_2 \):
1. Plug in the known values into the area formula:
\[ 126 = \frac{1}{2} \times 9 \times (13 + b_2) \]
2. Simplify the equation by multiplying both sides by 2 to get rid of the fraction:
\[ 126 \times 2 = 9 \times (13 + b_2) \]
\[ 252 = 9 \times (13 + b_2) \]
3. Divide both sides by the height (9 feet) to isolate the expression in parentheses:
\[ \frac{252}{9} = 13 + b_2 \]
\[ 28 = 13 + b_2 \]
4. Solve for \( b_2 \) by subtracting 13 from both sides of the equation:
\[ 28 - 13 = b_2 \]
\[ 15 = b_2 \]
The length of the second base \( b_2 \) is therefore 15 feet.
