Question

find the length of the diagonal of the prism. (1 point) cm

Explanation:

Step1: Find the diagonal of the base

Use the Pythagorean theorem \(d_{base}^2 = l^2+w^2\), where \(l = 3\) cm and \(w = 4\) cm.
\(d_{base}^2=3^2 + 4^2=9 + 16=25\), so \(d_{base}=5\) cm.

Step2: Find the space - diagonal of the prism

Use the Pythagorean theorem again for the right - triangle formed by the base - diagonal (\(d_{base}=5\) cm) and the height (\(h = 12\) cm) of the prism. Let the space - diagonal be \(d\).
\(d^2=d_{base}^2+h^2\)
Substitute \(d_{base}=5\) and \(h = 12\) into the formula: \(d^2=5^2+12^2=25 + 144=169\)
Take the square root of both sides: \(d=\sqrt{169}=13\)

Answer:

\(13\)