Question

Find $x$x​ . Square pyramid is shown with an altitude of 24 feet, drawn from the vertex to the base center, forming right angle. An apothem, labeled 10 feet is drawn from the base center to the midpoint of a base edge. Another altitude, labeled x is drawn from the vertex to the midpoint, forming right angle with the base edge. $x=$x=​ ft

Answer 1

x = 26feet

Explanation:

The three side length given forms a right angled triangle with the slant height of the pyramid labelled x.

Given

height of prism H = 24feet

Apothem a = 10feet

Required

Slant height x

Using the relationship according to Pythagoras theorem:

x² = H²+a²

Substitute the values

x² = 24²+10²

x² = 576+100

x² = 676

x = √676

x = 26

Hence the length labeled x is 26feet