Answer:
400 units³
Step-by-step explanation:
The volume (V) of the square pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
where h is the perpendicular height.
Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )
Using Pythagoras' identity on the right triangle
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
Area of square base = 10² = 100, hence
V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400
