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The base of a pyramid is a square of side 8cm. If its vertex...

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\(\sqrt3\)cm

A.

6cm

B.

5cm

C.

4cm

D.

3cm

Correct answer is C

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