Different Parts of Pyramid and Their Relationship

A diagram of square based pyramid is given below. Study the given diagram and discuss the following questions:

Here, 'e', 'l', 'h' and 'a' denote the edge, slant height, vertical height and the length of edge of base respectively.

e — Edge (lateral edge from apex to base corner)
l — Slant height (apex to midpoint of base edge)
h — Vertical height (apex perpendicular to base centre)
a — Length of base edge
O — Centre of base  |  M — Midpoint of BC

Now, from the diagram,

In the right angled triangle POM,
(PM)2 = (PO)2 + (OM)2 [∵ According to the Pythagoras theorem]
l2 = h2 + (
a2
)2
[OM =
12
AB =
12
a]
Similarly, in the right angled triangle PMC,
(PC)2 = (PM)2 + (MC)2 [∵ According to the Pythagoras theorem]
e2 = l2 + (
a2
)2
[MC =
12
BC =
12
a]