A square pyramid of base edge 10 centimetres and height 12 centimetres is to be made of paper. What should be the dimension of the triangles?

Can we make a square pyramid with the lateral surface area equal to the base area?

Using a square and four triangles with dimensions as specified in the picture, a pyramid is made.

What is the height of this pyramid?

What if the square and triangles are like this?

Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

A square pyramid is to be made with the triangle shown here as a lateral face. What would be its height? What if the base edge is 40 centimetres instead of 30 centimetres?