Geometry's a challenge

1-2: What is the apothem of a regular heptagon with a side of 10 and an area that is equal to the area of a hexagon? -- The regular hexagon has a side of 12. (tough?)

3-4. What is needed to find the volume of a pyramid, slant height or height? What about a cone?

5. What is the formula you use to find the area of a rhombus?

Originally posted by Ramned
1-2: What is the apothem of a regular heptagon with a side of 10 and an area that is equal to the area of a hexagon? -- The regular hexagon has a side of 12. ([b]tough?)

3-4. What is needed to find the volume of a pyramid, slant height or height? What about a cone?

5. What is the formula you use to find the area of a rhombus?[/b]

1-2. well...area = apothem times perimeter divided by 2. so...

Area of this hexagon would be... (6) 1/2 * b * h of one triangle derived from a hexagon being 6 equplateral traingles emanating from one center point.

area of the hexagon is 374.12.

side of hept = 10 * 7 sides = 70 total units = P

AP/2 = Area = Area of hex.

AP/2 = 374.12

A(70)/2 = 374.12

35A = 374.12

Apothem = 374.12/35 = 10.6892278

(not tough at all)

3-4. To find the volume of a pyramid you need height from base to apex and area of the base. Slant height is used in finding surface area of a pyramid.

In a cone you need radius (to find the area of the base) and height.

5. area of a rhombus is bh. (base * height)

Originally posted by EinsteinMind
1-2. well...area = apothem times perimeter divided by 2. so...

Area of this hexagon would be... (6) 1/2 * b * h of one triangle derived from a hexagon being 6 equplateral traingles emanating from one center point.

area of the hexagon is 374.12.

side of hept = 10 * 7 sides = 70 total units = P

AP/2 = Area = Area of hex.

AP/2 = 374.12

A( ...[text shortened]... radius (to find the area of the base) and height.

5. area of a rhombus is bh. (base * height)

You partially missed 1-2, but you got the others.
(Hint, did I say to round off?)

Originally posted by Ramned
You partially missed 1-2, but you got the others.
(Hint, did I say to round off?)

You lose, Ramned!

10.6891[428571]

the [428571] has a bar on top of it because it is a repeating decimal!

(I just don't know how to put the bar on top of something. Sorry. 😳 )

Originally posted by EinsteinMind
You lose, Ramned!

10.6891[428571]

the [428571] has a bar on top of it because it is a repeating decimal!

(I just don't know how to put the bar on top of something. Sorry. 😳 )

That is still rounded! Go ahead, keep typing that pattern, but no matter how many times you do it, you will be rounding. I said not to round. I want the exact number, so decimal won't work 😵

Originally posted by Ramned
That is still rounded! Go ahead, keep typing that pattern, but no matter how many times you do it, you will be rounding. I said not to round. I want the exact number, so decimal won't work 😵

The exact number is 10 and 24/35. Thank you.

Originally posted by EinsteinMind
The exact number???

I already gave the exact number!!!


it's 374.12/35

I think 374 12/35 would be proper, without the ".".

Originally posted by kbaumen
I think 374 12/35 would be proper, without the ".".

The exact number is 10 + 24/35

Originally posted by Ramned
That is still rounded! Go ahead, keep typing that pattern, but no matter how many times you do it, you will be rounding. I said not to round. I want the exact number, so decimal won't work 😵

It is not rounded, repeating decimals are exact numbers. The bar doesn't mean "keep writing out this string of numbers until your hand gets tired", it means "this string of numbers repeats an infinite number of times". As proof, try writing a number that fits between 0.[9] and 1.

EDIT: Borrowing EisteinMind's notation where 0.[9] = 0.99999...

Originally posted by EinsteinMind
The exact number is 10 + 24/35

Wrong.
If you tell me that decimal with the bar over it, it is not the EXACT answer. There is a difference between exact and decimal notation. While you took the correct steps to solving the problem, you are not doing it in exact numbers.

Nobody has gotten 1/2 correct yet. But to hint, Mr. Einstein took the correct steps. No decimal answer is accepted on this problem.

Maybe this is a tougher problem after all!

Originally posted by Ramned
Wrong.
If you tell me that decimal with the bar over it, it is not the EXACT answer. There is a difference between exact and decimal notation. While you took the correct steps to solving the problem, you are not doing it in exact numbers.

Nobody has gotten 1/2 correct yet. But to hint, Mr. Einstein took the correct steps. No decimal answer is accepted on this problem.

Maybe this is a tougher problem after all!

The question is flawed. You can't specify that the area of the heptagon is equal to the area of the hexagon AND specify the side length of the heptagon arbitrarily. For example, if you carry out the calculations using the side lengths provided, you find that the area of the hexagon is 216*SQRT(3), approximately equal to 374.12, and the area of the heptagon is 175/TAN(pi/7), approximately equal to 363.39.

Originally posted by PBE6
The question is flawed. You can't specify that the area of the heptagon is equal to the area of the hexagon AND specify the side length of the heptagon arbitrarily. For example, if you carry out the calculations using the side lengths provided, you find that the area of the hexagon is 216*SQRT(3), approximately equal to 374.12, and the area of the heptagon is 175/TAN(pi/7), approximately equal to 363.39.

Thank you, PB. I am trying to get an exact number but repeating decimals are indeed exact.

Plus you say that neither decimals nor fractions are exact.

What do you want Ramned? do you want to get cursed at? because that's what I'm about to do.

Originally posted by EinsteinMind
Thank you, PB. I am trying to get an exact number but repeating decimals are indeed exact.

Agreed!

Originally posted by EinsteinMind
Thank you, PB. I am trying to get an exact number but repeating decimals are indeed exact.

Plus you say that neither decimals nor fractions are exact.

What do you want Ramned? do you want to get cursed at? because that's what I'm about to do.

The fraction you gave me was wrong and the repeating decimal you gave me was wrong! So maybe it isn't a repeating decimal. 10 + 24/35 is not correct. And neither is that repeating decimal you showed me.

So give the answer in radical form. That's what I've been trying to get at. I haven't been arguing over the fact that repeating decimals are not exact. Whatever decimal you gave me, I assure you was not right.

Originally posted by Ramned
The fraction you gave me was wrong and the repeating decimal you gave me was wrong! So maybe it isn't a repeating decimal. 10 + 24/35 is not correct. And neither is that repeating decimal you showed me.

So give the answer in radical form. That's what I've been trying to get at. I haven't been arguing over the fact that repeating decimals are not exact. Whatever decimal you gave me, I assure you was not right.

So it's 216 times the square root of three divided by 35.



Ok so the decimal was not right.




Damn you.