To find the height of a pyramid with a square base given that its gradient (slope) is 4, we can use the following relationship:

The gradient of the pyramid can be expressed as the ratio of the height ($h$) to half the side length of the base.

Step-by-step solution:

1. Base of the pyramid:

   • Each side of the square base is $20 \, \text{cm}$.
   • Half the side length of the base is $\frac{20}{2} = 10 \, \text{cm}$.

2. Gradient formula: The gradient of the pyramid is the ratio of the height ($h$) to half the side length of the base: $\text{Gradient} = \frac{h}{10}$ We know that the gradient is 4: $4 = \frac{h}{10}$

3. Solving for height: Multiply both sides by 10 to isolate $h$: $h = 4 \times 10 = 40 \, \text{cm}$

Answer:

The height of the pyramid is 40 cm.

Would you like more details on this, or do you have any questions?

Here are 5 related questions you might find interesting:

1. How would the height change if the base was a rectangle instead of a square?
2. How do you calculate the volume of this pyramid?
3. What would the gradient be if the height was halved?
4. How does the surface area of the pyramid change as the height increases?
5. How would the height be affected if the gradient doubled?

Tip: For pyramids, the gradient is directly related to the slope of the sides and helps in finding various geometric properties like height and slant height.