Serious and Easy Question: Why does the land size in this example increase?

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froot

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Which option or "formula" from below do I use to find the total land area AND WHY? >>>>>PLEASE STATE AND EXPLAIN WHY IT'S USED OVER THE OTHERS<<<<<

find total land area, find percentage of ocean

Known information:

2d map world size = 512 x 512km = 262,144,000,000m2

Continent 1 of 3
28% of total land mass area
192x96km
18,432,000,000m2

a=28%
b=x
c=y

a+b+c=100%

option one:
b+c=100-28
b+c= 72

difference of 28 and 72 = 44

192x0.44+192= 276.48
96x0.44+96= 138.24

total 276.48+192= 468.48
138.24+96= 234.24

468.48x234.24= [109,736,755,200m2]

option two:
72/2 = 36

36-28=8

192x0.08+192=207.36
96x0.08+96=103.68

207.36x2=414.72
103.68x2=207.36

414.72x207.36 = 85,996,339,200 + 18,432,000,000m2 = [104,428,339,200m2]

option 3:
18,432,000,000m2 / .28 = 65,828,571,428m2 + 18,432,000,000m2 = [84,260,571,428m2]

option 4:
difference of 72%

192x0.72+192=330.24
96x0.72+96=165.12

330.24x165.12 = 54,529,228,800 + 18,432,000,000 = [72,961,228,000m2]

option 5:
192km / .28 = 685.71...
96km / .28 = 342.85...

685.71x342.85 = [234,270,000,000m2]
 
Last edited:
froot said:
Which option or "formula" from below do I use to find the total land area AND WHY? >>>>>PLEASE STATE AND EXPLAIN WHY IT'S USED OVER THE OTHERS<<<<<

find total land area, find percentage of ocean

Known information:

2d map world size = 512 x 512km = 262,144,000,000m2

Continent 1 of 3
28% of total land mass area
192x96km
18,432,000,000m2

a=28%
b=x
c=y

a+b+c=100%

option one:
b+c=100-28
b+c= 72

difference of 28 and 72 = 44

192x0.44+192= 276.48
96x0.44+96= 138.24

total 276.48+192= 468.48
138.24+96= 234.24

468.48x234.24
[109,736,755,200m2]

option two:
72/2 = 36

36-28=8

192x0.08+192=207.36
96x0.08+96=103.68

207.36x2=414.72
103.68x2=207.36

414.72x207.36 = 85,996,339,200 + 18,432,000,000m2 = [104,428,339,200m2]

option 3:
18,432,000,000m2 / .28 = 65,828,571,428m2 + 18,432,000,000m2 = [84,260,571,428m2]

option 4:
difference of 72%

192x0.72+192=330.24
96x0.72+96=165.12

330.24x165.12 = 54,529,228,800 + 18,432,000,000 = [72,961,228,000m2]
Click to expand...
Exactly where are you confused?!
 
Neither approach makes any sense.

You seem, in both, to be finding the percent increase in area from continent A to either B and C together, or their average. Then you are applying that percent increase to the linear dimensions of A. That is nonsense: areas are not proportional to both linear dimensions.

If you want to do anything like what you are doing, you need to look not at percent increases, but at ratios; and use the square root of the ratio of areas to find the ratio of sides.

But I don't see why you are doing any of that. If 18,432 square km is 28% of the land area, then to find the total land area you just need to solve the equation 18,432 = 0.28x. (This is similar to option 3, which I didn't notice at first; but that is not quite right.)

Also, if this were a round world, you couldn't measure areas by multiplying length and width, and a flat map couldn't measure both areas and distances correctly; I assume this is meant to be a flat world?
 
Dr.Peterson said:
Neither approach makes any sense.

You seem, in both, to be finding the percent increase in area from continent A to either B and C together, or their average. Then you are applying that percent increase to the linear dimensions of A. That is nonsense: areas are not proportional to both linear dimensions.

If you want to do anything like what you are doing, you need to look not at percent increases, but at ratios; and use the square root of the ratio of areas to find the ratio of sides.

But I don't see why you are doing any of that. If 18,432 square km is 28% of the land area, then to find the total land area you just need to solve the equation 18,432 = 0.28x. (This is similar to option 3, which I didn't notice at first; but that is not quite right.)

Also, if this were a round world, you couldn't measure areas by multiplying length and width, and a flat map couldn't measure both areas and distances correctly; I assume this is meant to be a flat world?
Click to expand...

I don't see how it's a problem to say that the first continent is 28% of the total land area, and the other two who are equal to eachother would give a 72% remainder out of obviously 100% land area.

What do you mean when you say option 3 is not quite right?

'2d world map' as seen near the top of the OP.

What would be the correct way, and why?
 
froot said:
option 3:
18,432,000,000m2 / .28 = 65,828,571,428m2 + 18,432,000,000m2 = [84,260,571,428m2]
Click to expand...

Check your answer. Is 28% of 84,260,571,428 equal to 18,432,000,000?

I told you the correct way; you did that, but then did more. I think you are too familiar with percent increases, and forgot that the 28% is not an increase, just a percentage.
 
Why does the land size in this example increase?

I made a video here. Shows all the steps involved. And it's good because it allows you to picture everything.
Please reference the video, and give your input.

[video=youtube;rNA_0Y9uqks]https://www.youtube.com/watch?v=rNA_0Y9uqks[/video]
 
Dr.Peterson said:
Check your answer. Is 28% of 84,260,571,428 equal to 18,432,000,000?

I told you the correct way; you did that, but then did more. I think you are too familiar with percent increases, and forgot that the 28% is not an increase, just a percentage.
Click to expand...


Okay. What about, as the total is 84,260km2 = 290.27573098693593678320515581144 km x 290.27573098693593678320515581144 km (as square root)

Knowing the first land mass is 192x96 km, and the other two are larger (I'm not going to be accurate here as it's not the point; 206x105km)...
You now have 192x96 km + 206x105km + 206x105 km.

Adding them up.

192+206+206 = 604
96+105+105 = 306

so now together they are 604x306 km... Which goes over the 290km x 290km above. And now I'm confused.

Also dividing the 84260 by 3 gives

84260 / 3 = 28086.666666666666666666666666667

Sq 28086.66.... = 167.5907714245228559944002268628 x 167.5907714245228559944002268628
167.6 (3) = 502.8 x 502.8

And that doesn't make sense either, as the whole map is only 512 x 512 km
 
Last edited:
froot said:
Okay. What about, as the total is 84,260km2 = 290.27573098693593678320515581144 km x 290.27573098693593678320515581144 km (as square root)

Knowing the first land mass is 192x96 km, and the other two are larger (I'm not going to be accurate here as it's not the point; 206x105km)...
You now have 192x96 km + 206x105km + 206x105 km.

Adding them up.

192+206+206 = 604
96+105+105 = 306

so now together they are 604x306 km... Which goes over the 290km x 290km above. And now I'm confused.

Also dividing the 84260 by 3 gives

84260 / 3 = 28086.666666666666666666666666667

Sq 28086.66.... = 167.5907714245228559944002268628 x 167.5907714245228559944002268628
167.6 (3) = 502.8 x 502.8

And that doesn't make sense either, as the whole map is only 512 x 512 km
Click to expand...

It seems to me that you're trying to do a lot more than the original question (find the total land area). Let's just look at the various things you are saying, and try to cover it all.

First, the answer to the question is simply 18,432/.28 = 65828.57 km2; the check is that 28% of this is 18,432 km2. Your 84,260, as I said, is wrong. You added the first continent to the total area.

Now, your total world (map) has an area of 512*512 = 262,144 km2. So the total land area is 65,828.57/262,144 = 25.11% of the world.

Now let's back up and look at the whole picture.

The basic data you've provided, as I understand it, are

World size: 512 km x 512 km = 262,144 km2
Continent 1: 192 km x 96 km = 18,432 km2
Continent 2: 206 km x 105 km = 21,630 km2
Continent 3: 206 km x 105 km = 21,630 km2
Total land: 61,692 km2

I'm assuming that these continents are actually rectangles as you imply, not irregular blobs as usual, whose area would be harder to find.

Now, the total land area I just calculated here is not what we got above from the 28% assumption; in fact, continent 1 is really 18,432/61,692 = 30% of total land area. Where did your 28% come from? It seems to be wrong, but maybe somewhere in here things have been approximated.

Through much of what you've written have been misunderstandings about how area works. Above, you said the total land area is 192x96 km + 206x105 km + 206x105 km, but rather than add those areas, you added individual lengths and widths, "192+206+206 = 604 and 96+105+105 = 306". Areas don't add by adding sides; they add by adding the areas themselves. If you made a rectangle 604 by 306, you could fit your three smaller rectangles into it, with a lot more room. Here is an attempt to show what that would look like:

Code: 
[FONT=courier new] 192  206  206[/FONT]
[FONT=courier new]+---+----+----+
|:::|         |96
+---+----+    |
|   |::::|    |105
+   +----+----+
|        |::::|105
+--------+----+[/FONT]

The "shaded" areas are the three continents; the whole big rectangle is the area you found, which clearly is much bigger than the sum of the three.
 
Sorry, but can't read the video text. The image is too small, and the forum platform doesn't let us enlarge the view screen. Try a different technique to convey the questions.
 
I took the time to watch the video, and as I expected, your question is essentially what I answered in my 8:20 post on your other thread.
FMH111262 video snip.jpg
The total area of two rectangles is found by adding their areas: 303*94 + 512*303 = 28482 + 155136 = 183618. It is not the area of the rectangle formed by adding the lengths and the widths, (303 + 512)*(94 + 303) = 815*397 = 323555.

Try sketching this larger rectangle, and you can see what is happening. Or recall your algebra, and "FOIL" the product (303 + 512)*(94 + 303) to see how it compares to 303*94 + 512*303.
 
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