Square Pyramid: Underlying Anatomy

Interact with this square pyramid for a minute or two. You can alter the base and height of this square pyramid by dragging the 2 white points. How would you describe the relationship between a square pyramid's LATERAL HEIGHT and its TRUE HEIGHT?

Suppose each edge of the square base measures 10 cm. If this square pyramid's lateral height measures 13 cm, what would its true height be? What would the pyramid's lateral area be? What would its total surface area be? What would its volume be?