A stop sign is a regular octagon. This stop sign has a height of 30 inches and each side is 12.43 inches. The area of a 30-inch sign is ____ in2 to the nearest square inch. (Enter only the number.)

Question

anonymous · Answer

|dw:1360803282891:dw|

whpalmer4 · Answer

Do you know a formula for the area of a regular octagon?

anonymous · Answer

Area of a octagon =

anonymous · Answer

Oh it didn't... hold on ahah

anonymous · Answer

Let S = the length of the side of the octagon.

Let A = the area of the octagon

Then A = 2(1+ sqrt2)xS^2 = 4.828 S^2

whpalmer4 · Answer

You can look up such a formula, or we can figure it out.  Because this is a regular octagon, we can divide it up into a bunch of isoceles triangles with their apex at the center, and the base being the outside edges.

whpalmer4 · Answer

That'd be great, if only we knew the side length of the octagon.  Do you see a way to figure it out?

anonymous · Answer

Lol it says in the question 12.43

whpalmer4 · Answer

Great!  That's the easiest way to find it :-)

whpalmer4 · Answer

What's your answer for the area?

anonymous · Answer

I have to multiply 12.43 times 12.43 right?

whpalmer4 · Answer

Yes.  You'll be evaluating 

$$A=2(1+\sqrt{2})(S)^2 \approx 4.828*12.43*12.43 =$$

anonymous · Answer

12.43x12.43=154.5049

whpalmer4 · Answer

Agreed

whpalmer4 · Answer

But that's not the final answer...

anonymous · Answer

I know...I suck at math I need my hand held in it Lol

whpalmer4 · Answer

$$A = 4.828*12.43*12.43 = 4.828*154.5049 =$$

anonymous · Answer

so 4.828x154.5049 and the sum of that is the answer?

whpalmer4 · Answer

Multiply 4.828 * 154.5049.  The number you get (the product), rounded to the nearest square inch, is the answer.

whpalmer4 · Answer

The 4.828 replaces the $2(1+\sqrt{2})$ in the formula.

anonymous · Answer

Okay so I got 745.9496572

whpalmer4 · Answer

Yes, that's the product of those numbers, but not your answer... "rounded to the nearest square inch"

anonymous · Answer

Haha I love your patience.  As you can see I suck at math I'm like a 5 year old... How do you "round to the nearest square inch" .__. I feel dumb haha :P

whpalmer4 · Answer

Okay, to round a number, you look at the next digit after the spot you are rounding to.  If it is 5 or larger, you round your number up and zero out everything to the right.  If it is 0-4, you just zero out everything to the right.

Some examples:

53 rounded to the nearest 10:
Look at the 3 in the 1s place, that's less than 5, so our answer is 50.

57 rounded to the nearest 10:
Look at the 7 in the 1s place, that's 5 or greater, so our answer is 60.

2.41 rounded to the nearest 0.1:
Look at the 1 in the .01 place, that's less than 5, so our answer is 2.4

2.45 rounded to the nearest 0.1:
Look at the 5 in the .01 place, that's 5 or greater, so our answer is 2.5

Does that make sense?  Prove it by rounding off the answer correctly :-)

anonymous · Answer

745.90?

whpalmer4 · Answer

No.  Isn't the nearest square inch going to be a nice round number like 756 or 835, and not have a decimal after it?  How do you read that number?  Seven hundred forty-five and 90 one-hundredths.  Sounds like there's a fraction in there, doesn't it?