To calculate the length of $DE$ in the cuboid, we will use the Pythagorean theorem in two stages:

Step 1: Calculate $AC$ (the diagonal of the base rectangle)

The dimensions of the base rectangle $ABCD$ are:

• $AB = 18 \, \text{cm}$,
• $AD = 22 \, \text{cm}$.

Using the Pythagorean theorem: $AC = \sqrt{AB^2 + AD^2}$ $AC = \sqrt{18^2 + 22^2}$ $AC = \sqrt{324 + 484} = \sqrt{808}$ $AC \approx 28.4 \, \text{cm}$

Step 2: Calculate $DE$ (the diagonal of the cuboid)

The dimensions involved are:

• $AC \approx 28.4 \, \text{cm}$ (from Step 1),
• $DE = \sqrt{AC^2 + height^2}$, where height $= 4 \, \text{cm}$.

Using the Pythagorean theorem: $DE = \sqrt{AC^2 + height^2}$ $DE = \sqrt{28.4^2 + 4^2}$ $DE = \sqrt{807.56 + 16} = \sqrt{823.56}$ $DE \approx 28.7 \, \text{cm}$

Final Answer:

The length of $DE$ is approximately 28.7 cm to 1 decimal place.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. How would the result change if the height of the cuboid increased to 6 cm?
2. Can you calculate the total surface area of the cuboid?
3. How do you calculate the length of $BF$, another diagonal of the cuboid?
4. What is the formula for finding the volume of this cuboid?
5. How would you verify the calculation for $DE$ without a calculator?

Tip: Always double-check your intermediate calculations for accuracy when solving multi-step problems!