To find the length of the diagonal of a prism, we can use the Pythagorean theorem. For a rectangular prism, the diagonal \( d \) can be determined with the formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
In your case, you have:
- Height (\( h \)) = 12 cm
- Base dimensions (\( l \) = 4 cm, \( w \) = 3 cm)
Let's plug these values into the formula:
\[ d = \sqrt{4^2 + 3^2 + 12^2} \]
Calculating the squares:
\[ d = \sqrt{16 + 9 + 144} \]
Now, add those values:
\[ d = \sqrt{169} \]
Finally, take the square root:
\[ d = 13 \text{ cm} \]
The length of the diagonal of the prism is 13 cm.
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