To find the worth of the rectangular sheet of metal, we first need to calculate its area. The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{width} \]
For this sheet of metal, the dimensions are 8 inches and 11 inches. Thus, the area is:
\[ A = 8 , \text{inches} \times 11 , \text{inches} = 88 , \text{square inches} \]
Next, we need to calculate the total value of this area, knowing that the metal is worth $0.13 per square inch. We can calculate the total worth \( W \) by multiplying the area by the price per square inch:
\[ W = A \times \text{price per square inch} = 88 , \text{square inches} \times 0.13 , \text{dollars per square inch} \]
Calculating this:
\[ W = 88 \times 0.13 = 11.44 , \text{dollars} \]
Thus, the sheet of metal is worth:
\[ \boxed{11.44} , \text{dollars} \]