Math Is Fun Forum / area review

zee-f · 2012-11-30 07:25:18

Hi,

I really need help seeing if I answered correctly:

1. If a hexagon has a side of 3 units, what is the area of the hexagon?

#1- 3² * 6 / 4* Tan(180/6) = 27√3/2 = 23.38

bobbym · 2012-11-30 08:41:01

Hi;

For a regular hexagon.

Where s is a side.

Your answeer is correct!

zee-f · 2012-11-30 09:34:45

Thank you

Ok am stuck on this one
If a hexagon has an area of 100 units, what is the length of one side?

So the equation would be : 100= 3√3 / 2 * s² right?

bobbym · 2012-11-30 09:43:41

Hi;

Yes, that is correct. Need some help solving that?

zee-f · 2012-11-30 10:05:31

yeah am stuck on where to start

bobbym · 2012-11-30 10:32:00

Hi;

Divide on both sides by that constant.

Convert it to decimal, not necessary but will make it a bit easier for you.

How about now?

zee-f · 2012-12-01 02:53:11

Thank you so so much....

Ok I solved the following using formulas I know and the formula you used :

3. If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?

3. Ok I need to find the area to get the side. So I know that if I have the radius I can find the area by doing the following : A = r² * N * sin(360/n) / 2
A= 6² * 6 * sin(360/6) / 2 = 93.53074361

I know that area = 3 sqrt(3) / 2 * side² So S= 93.53074361 / 3sqrt(3)/2 which equales 36 So the side of the hexogon = 36

4. If a hexagon has a radius (center to point of angle) of 6, what is the area of the hexagon?

4. A = r² * N * sin(360/n) / 2
A= 6² * 6 * sin(360/6) / 2 = 93.53074361
So the area of the hexagon = 93.53074361

5. If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?

5. Ok I need to find the area to get the length of each side . If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)
area= 9^2 * 6 * tan * (180/6) = 280.59
So I know that the area for a regular hexagon = 3SQRT(3) / 2 multipliyed by S^2
280.59 = 3SQRT(3) /2 * S^2
S^2 = 280.59 / 3SQRT (3) = 81

So the length of each side of the hexagon = 81

6. If a hexagon is resting on a flat side, and has a total height of 18, what is the area of the hexagon?

6- If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)
area= 9^2 * 6 * tan * (180/6) = 280.59

Last edited by zee-f (2012-12-01 03:03:01)

bob bundy · 2012-12-01 03:22:37

hi zee-f

3. If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?

3. Ok I need to find the area to get the side. So I know that if I have the radius I can find the area by doing the following : A = r² * N * sin(360/n) / 2
A= 6² * 6 * sin(360/6) / 2 = 93.53074361

I know that area = 3 sqrt(3) / 2 * side² So S= 93.53074361 / 3sqrt(3)/2 which equales 36 So the side of the hexogon = 36

You mean side^2 = 36 so side = √ 36

method perfectly correct, but you've gone the long way to get this. A regular hexagon is made up of 6 equilateral triangles, so, if the radius is 6, so are the sides.

4. If a hexagon has a radius (center to point of angle) of 6, what is the area of the hexagon?

4. A = r² * N * sin(360/n) / 2
A= 6² * 6 * sin(360/6) / 2 = 93.53074361
So the area of the hexagon = 93.53074361

Correct!

5. If a hexagon is resting on a flat side, and has a total height of 18, what is the length of each side of the hexagon?

5. Ok I need to find the area to get the length of each side . If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)
area= 9^2 * 6 * tan * (180/6) = 280.59
So I know that the area for a regular hexagon = 3SQRT(3) / 2 multipliyed by S^2
280.59 = 3SQRT(3) /2 * S^2
S^2 = 280.59 / 3SQRT (3) = 81

So the length of each side of the hexagon = 81

This is way too big for H=18. I wonder what went wrong?

area calculation looks ok.

so I think it's the second part that's gone wrong

area = 0.5 x side x side x sin60 x 6

sin60 =√ 3 /2 so that looks good too.

6. If a hexagon is resting on a flat side, and has a total height of 18, what is the area of the hexagon?

6- If H is 18 that means the apothem equales 9 So that means the area = A^2 * N * tan * (180/n)
area= 9^2 * 6 * tan * (180/6) = 280.59

Correct!

Bob

zee-f · 2012-12-01 08:11:21

5. OK I need to find the area to get the length of each side . If H is 18 that means the apothem equals 9 So that means the area = A^2 * N * tan * (180/n)
area= 9^2 * 6 * tan * (180/6) = 280.59

3 (√3 /2) * S² = 280.59 ======> s² = 280.59 * 2 / 3 * √3 = 107.9991414

bob bundy · 2012-12-01 09:36:35

Good ... so s = ???

Bob

zee-f · 2012-12-01 12:25:52

s= 10.39226354

bob bundy · 2012-12-01 19:08:30

Excellent! That's what I make it too.

Bob

zee-f · 2012-12-02 02:58:30

Thank you guys

zee-f · 2012-12-02 02:59:43

This is the last question am stuck on

7. Come up with a way to find the area and volume of a football. Include in your answer a way to acquire any necessary measurements without cutting or otherwise destroying the football. Also include all necessary formulas to implement your idea. (You don't need to find actual numbers, just outline the method in step by step detail--think of all the measurements you'll need to acquire and how you'll get them.)

7. ok So a football looks like two cones attached So I can uses the same formula I use for a cone right?

bob bundy · 2012-12-02 05:39:29

hi zee-f

That's a different thing to ask. There won't be one correct answer here ... just think of a good method.

The double cone idea would give you an fairly good answer. But the solid is not quite right (see first two pictures below).

My idea for the volume is illustrated by the third picture. Can you see what you'd have to do?

This would give a fairly good answer if you measured carefully.

The surface area is somewhat harder.

I'd get a ball and some cm square paper (or inch square) and cut out pieces to stick onto the surface with the aim of covering it as well as possible.

If you want to answer with the double cone method then you'll have to explain what measurements are needed and what formula to use.

Bob

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zee-f · 2012-12-03 03:43:03

I would measure the height using a tape measure then half the height I would draw a line around the circle and measure the height across and divide it by 2 and use that as a radius

zee-f · 2012-12-03 03:44:10

Volume = π × r2 × (h/3)

bob bundy · 2012-12-03 05:12:20

hi zee-f

I would draw a line around the circle and measure the height across and divide it by 2 and use that as a radius

a line around will give you the circumference not the diameter.

Volume = π × r2 × (h/3)

r^2 when you have the radius correctly.

then double for two cones,

Bob

zee-f · 2012-12-03 07:28:13

ok since (C=pD) I would divide the circumference by PI to get D then divide it by 2 to get R

bob bundy · 2012-12-03 09:11:27

That's right.

Bob

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#1 2012-11-30 07:25:18

area review

#2 2012-11-30 08:41:01

Re: area review

#3 2012-11-30 09:34:45

Re: area review

#4 2012-11-30 09:43:41

Re: area review

#5 2012-11-30 10:05:31

Re: area review

#6 2012-11-30 10:32:00

Re: area review

#7 2012-12-01 02:53:11

Re: area review

#8 2012-12-01 03:22:37

Re: area review

#9 2012-12-01 08:11:21

Re: area review

#10 2012-12-01 09:36:35

Re: area review

#11 2012-12-01 12:25:52

Re: area review

#12 2012-12-01 19:08:30

Re: area review

#13 2012-12-02 02:58:30

Re: area review

#14 2012-12-02 02:59:43

Re: area review

#15 2012-12-02 05:39:29

Re: area review

#16 2012-12-03 03:43:03

Re: area review

#17 2012-12-03 03:44:10

Re: area review

#18 2012-12-03 05:12:20

Re: area review

#19 2012-12-03 07:28:13

Re: area review

#20 2012-12-03 09:11:27

Re: area review

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