Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem twice. First, find the diagonal of the base rectangle (NP), and then use that diagonal along with the height of the rectangular prism to find the length of the space diagonal NK.

 

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths and and hypotenuse of length , . This theorem helps in finding the lengths of unknown sides in right - triangles, which is crucial for determining the diagonal lengths in this rectangular prism.

 

Step - by - Step Solution

1. Find the length of the diagonal of the base rectangle (NP):

In the base rectangle NOPQ, cm and cm.

By the Pythagorean Theorem, .

Substitute the values: .

Calculate and .

Then .

Take the square root,

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