Answer:
16.6 in
Step-by-step explanation:
The volume (V) of a pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × h
where h is the perpendicular height and area of base = 14² = 196
here V = 980, so
[tex]\frac{1}{3}[/tex] × 196h = 980 ( multiply both sides by 3 )
196h = 2940 ( divide both sides by 196 )
h = 15
Consider the right triangle formed by the height h from the vertex to the midpoint of the base and the slant height (s) ← the hypotenuse
Using Pythagoras' identity in the right triangle
s² = 15² + 7² = 225 + 49 = 274 ( take the square root of both sides )
s = [tex]\sqrt{274}[/tex] ≈ 16.6
