To find the volume of a pyramid (or a triangular prism, as it seems like there might be a mix-up in terminology), we typically use the following formula for the volume of a pyramid:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the base of the prism is a rectangle with dimensions of 7 cm (width) and 10 cm (length), the area of the base is:
\[ \text{Base Area} = \text{Width} \times \text{Length} = 7 , \text{cm} \times 10 , \text{cm} = 70 , \text{cm}^2 \]
The height of the prism (as stated in the problem) is 11 cm.
Now we can calculate the volume:
\[ \text{Volume} = \frac{1}{3} \times 70 , \text{cm}^2 \times 11 , \text{cm} \]
Calculating this gives:
\[ \text{Volume} = \frac{1}{3} \times 770 , \text{cm}^3 = \frac{770}{3} , \text{cm}^3 \approx 256.67 , \text{cm}^3 \]
Thus, the volume of the prism is approximately 256.67 cm³.
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