Question

What's a method/expression to solve for serface area for 3d square pyramid

Answer 1

The surface area of a 3D square pyramid looks as shown in the following diagram:

To calculate the surface area, it is needed to find the area of the base of the pyramid which is the square at the center, and also the area of the triangles which are the sides of the pyramid and also are all equal.

Area of the base:

The area of the base is the length of the sides squared. If we call "l" the length of the sides:

`A_{\text{base}}=l^2`

Area of the triangles:

The formula to calculate the area of just one of the triangles is:

`A_{\text{triangle}}=(l* h)/(2)`

Where h is the height of the triangle, and l the side of the square:

And to find the area of the 4 triangles, we multiply the previous expression by 4:

`A_{\text{triangles}}=4*(l* h)/(2)`

We can divide 4 by 2 and the result is 2 multiplied by lxh:

`A_{\text{triangles}}=2(l* h)`

Thus, the surface area is:

`SA=A_{\text{base}}+A_{\text{triangles}}`
`SA=l^2+2(l* h)`

Answer:

The expression to find the surface area of a 3D square pyramid is:

`SA=l^2+2(l* h)`