The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4.3cm

The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4.3cm

Answer Details

Base of pyramid of a square of side 8cm vertex directly above the centre edge = $4\sqrt{3}$cm
From the diagram, the diagonal of one base is AC2 = 82 + 82
Ac2 = 64 + 64 = 128
AC = $8\sqrt{2}$
but OC = $\frac{1}{2}$AC = 8$\sqrt{\frac{2}{2}}$ = $4\sqrt{2}$cm
OE = h = height
h2 = ($4\sqrt{3}$)2
16 x 2 - 16 x 2
48 - 32 = 16
h = $\sqrt{16}$
= 4