Question 1074875
The slant height is the height of the equilateral triangles of sides 8 cm each, that are the sides of that pyramid.
(Of course, the base is also an equilateral triangles of sides 8 cm each).
The height can be calculated using the Pythagorean theorem,
or using trigonometry.
For any equilateral triangle,
the height is {{{sqrt(3)/2=about 0.866}}} times the length of the side.
{{{drawing(300,300,-1,11,-2,10,
green(triangle(0,0,5,0,5,8.66)),
green(rectangle(5,0,4.6,0.4)),
triangle(0,0,10,0,5,8.66),
locate(2.4,0.6,4),locate(7.4,0.6,4),
locate(2.5,4.4,8),locate(7.2,4.4,8),
locate(5.1,4.2,green(h))
)}}} for that triangle, the Pythagorean theorem says 
{{{4^2+h^2=8^2}}} , so {{{16+h^2=64}}} --> {{{h^2=64-16}}} --->. {{{h^2=48}}} --> {{{h=sqrt(48)}}} --> {{{h=approximately}}}{{{highlight(6.93)}}} (correct to 3 significant figures ).