A floor tile is a regular hexagon of side 8 cm. What is its area in square cm? (Take √3 = 1.73.)

Joining the centre to the six corners splits a regular hexagon into SIX equilateral triangles of the same side, so the area = $6\times$ (√3/4) $\times 8^2$ = (3√3/2) $\times 64=2.595\times 64=166.08$ sq cm. The trap 110.72 uses only four triangles, the number a rectangle's diagonals would give; 27.68 is one triangle alone, (1.73/4) $\times$ 64; 48 is the hexagon's PERIMETER, $6\times 8$, a length offered where an area was asked.