Question

there is a diagonal prism, the height is 12 cm, the base is 3cm and 4cm.
what is the length of the diagonal prism.

12
13
14

Answer 1

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**.