Surface area of square based pyramid

The following image shows a square based pyramid with labels.

Deriving the Surface Area (SA)

Let’s try to derive/prove the surface area pyramid above. It’s actually very simple.
At the bottom of this pyramid we have a square. We have labelled the widths of this square b. The area of just this square shape we know is b². Notice we also have a slant height labelled l. This is in-between the triangle so we can find the area of this triangle. The area of this triangle is (bxl)/2. But the total area for these triangles is 4x(bxl)/2 which must equal to 2(bl).
So the surface area of this square based pyramid is;

The above is the area formula to find the total surface area of a square based pyramid.