Answer:
one side = [tex]\frac{a\sqrt{2}}{2}[/tex]
Step-by-step explanation:
if you draw an octagon on a piece of paper, you can draw a square around it, you should be able to see a diagram of this attached, ignore the 6.
Let's say TP = a
since it's a regular octagon, TP = HT
and using the Pythagoras Theorem, we know a² + b² = c² and thus:
√(AT² + HA²) = HT
and since AT = HA which we will call x, the equation becomes:
√(2x²) = HT = a
rearrange the equation to solve for x and you get:
2x² = a²
x² = [tex]\frac{a^{2} }{2}[/tex]
x = [tex]\frac{a}{\sqrt{2}}[/tex]
which, if you rationalise the denominator, you get:
x = [tex]\frac{a\sqrt{2}}{2}[/tex]
