Answer:
The lateral height of the square base pyramid is 3 meters.
How to find the surface area of a cube and square pyramid?
A square pyramid and a cube have the same total surface area. The length of each side of the base of the square pyramid is 12 meters. The width of the cube is 6 meters. Therefore, let's find the lateral height of the square pyramid as follows:
Hence,
surface area of a cube = 6a²
where
a = side length of the cube
Hence,
surface area of a cube = 6 × 6²
surface area of a cube = 216 m²
Therefore, surface area of the square base pyramid = a² + 2al
where
a = side length of the base
l = slant height of the pyramid
Therefore, surface area of the square base pyramid = 12² + 2 × 12 × l
surface area of the square base pyramid = 144 + 24l
216 - 144 = 24l
72 = 24l
l = 72 / 24
l = 3 meters