Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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?

Sagot :

azkaa

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]

View image azkaa
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.