To find the area of the figure you're describing, we need to determine its overall shape. It sounds like you have a trapezoid where the lengths of the bases are each 6 feet, and the height is 13 feet.
The area \( A \) of a trapezoid is calculated using the formula:
\[ A = \frac{(b_1 + b_2)}{2} \times h \]
Where:
- \( b_1 \) and \( b_2 \) are the lengths of the two bases.
- \( h \) is the height.
In your case:
- \( b_1 = 6 \) feet
- \( b_2 = 6 \) feet
- \( h = 13 \) feet
Substituting these values into the formula gives:
\[ A = \frac{(6 + 6)}{2} \times 13 \]
Calculating it step by step:
\[ A = \frac{12}{2} \times 13 = 6 \times 13 = 78 \text{ square feet} \]
Since you mentioned the area should be between 100 and 114 square feet, it seems like there might be some misunderstanding or additional context needed concerning the dimension for \( x \).
Could it be that the height or one of the bases is expressed incorrectly or that there are additional parts of the trapezoid?
If \( x \) were to represent a dimension that leads to an area between 100 and 114 but not affecting the entire height, we would need more specifics on how \( x \) should be related to the shape.
If you can provide more detail or clarification about the problem, I'd be happy to help further.