Answer:
d = √122 ≈ 11.045
Explanation:
The diagonal of the top face of the prism is the diagonal of a rectangle with dimensions 8 and 7. Its square will be ...
(top face diagonal)^2 = 8^2 +7^2
The space diagonal 'd' will be the hypotenuse of a triangle that has one leg* equal to the height of the prism (3) and the other leg equal to the face diagonal. Using the Pythagorean theorem again, we have ...
d^2 = 3^2 +(top face diagonal)^2
Substituting for (top face diagonal)^2, we have ...
d^2 = 3^2 + 8^2 +7^2
d^2 = 9 +64 +49 = 122
d = √122 ≈ 11.045
_____
* The triangle we're talking about here is the right triangle with one leg from the bottom front corner to the top front corner. The other leg is the face diagonal from the top front corner to the top rear corner. The segment marked 'd' is the hypotenuse of this triangle.