Find the area of the lateral surface of a regular quadrangular pyramid if the side of the base is 6 dm and the apothem is 9 dm.

Given:
The pyramid is rectangular regular.
Apothema is 9 decimetres.
The base is 6 decimetres.

Let’s find the area of only one side of the pyramid, which is a triangle:
S = 1/2 * h * b = 1/2 * 9 * 6 = 27 dm2.
In total, the quadrangular regular pyramid has four sides, and they are all equal to each other.
We calculate the area of the entire lateral surface:
S = 27 * 4 = 108 dm2.
Answer: S = 108 dm2.