Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem twice. First, find the length of the diagonal of the base rectangle (EFHG), and then use that result along with the height of the cube to find the length of the space diagonal AF.

 

Key Concept Explanation

The Pythagorean Theorem states that for a right - triangle with legs of lengths  and  and hypotenuse of length , . This theorem is used to find the lengths of unknown sides in right - triangles, which is essential for solving for the diagonal lengths in this cube.

 

Step - by - Step Solution

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

In the base rectangle EFHG,  cm and  cm.

Using the Pythagorean Theorem, .

Substitute the values: .

Calculate  and .

Then .

Take the square root of both sides,

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