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

6cm

5cm

4cm

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

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