Question

A regular octagon with side length a cm can be made by cutting off

Answer 1

Answer:

one side = $\frac{a\sqrt{2}}{2}$

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 = $\frac{a^{2} }{2}$

x = $\frac{a}{\sqrt{2}}$

which, if you rationalise the denominator, you get:

x = $\frac{a\sqrt{2}}{2}$