Question

a regular octagon with side length a cm can be made by cutting off the four corners of a square board.how long should the sides of the board be​

Answer 1

Answer:

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

2

a

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}

2

a

2

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

2

a

which, if you rationalise the denominator, you get:

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

2

a

2