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good one

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After my research I am led to believe that many real life surface areas are found using satellite images or using beacons to calculate the general size of the area, and then from there more in depth triangulation can be used to find out the area. When rounding to a tenth of a km as they did in the example posted, you could use triangulation without using such small angles for example .01° as the small spaces missed when using a technique like this (for example 3m^2) would not even be recorded when measuring to the nearest tenth of a km.

- Ewan

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I'm thinking that the issue here is the level of math implied. This sounds like a very simplistic model and therefore there would likely be a good deal of error. The less like a rectangle the lake is... the greater the error. Dig a bit deeper and/or consider how you improved your model with the unit circle.

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Are you ready to give this a go today? I'm looking for a pack of seeds in the science dept.

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Can you print a map of lake Zug and a grid to give this a try?

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This was a clear example and thanks for including the link.

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So... can you do this using a map or via an online tool?

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this is what i found... I like the tracking points thing to get measurements but the height times width doesn't sound right... - Sophia

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Say you had a map of a country with map area

'Amap'. Throw a large number 'N' of small seeds randomly on the map. By the number of seeds to fall within the country 'n', one can find the area of the country:

Area of country= area of map times n/N

-Nelwin

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I found out that most lakes have the simple dimensions regular polygons have that are necessary to calculate area. These are the length and the width. The lake can then be broken into segments of squares and triangle and the individual areas can be calculated and added together to get the rough area. Using the Zug lake as a simplistic example, the top half could be seen as a rectangle and the bottom half as a triangle. When calculating exactly more shapes will be used to separate the lake however the method stays the same.

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How about a link to your and a photo. Could you be prepared to try this tomorrow? Find a grid online that we could copy onto transparency using the copier at school.
-Mr. Bond

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I found online that they can take aerial photos and with these photos they can then add in polygons to cover the desired area. They then mark each corner with a coordinate. From there they can then calculate the area selected with a formula.

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I think we should do this tomorrow. How about we measure the island of trees near the sports hall

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I found that if you have a map and put miniature squared paper on it. You can get quite accurate with the area of it as long as your squares are extremely small. This is quite practical and if you have a scaled map and do it on that, then you just multiply the area of the mini squares by the scale. For example if the scale is 1cm = 10km and one square on the paper is 1cm2 then you multiply the 1cm2 by 10 to find the real life answer in km.

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I found out that to calculate an area of a lake we need to overlay a piece of transparent paper on top of the map with the lake. Then we divide the shape into squares, triangle and semi-circles (divide area of a circle by two). From then on we add up the areas of all the shapes and we get the area of the lake.

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How about a link to share:)

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Using geometric shapes to calculate irregular shaped areas.

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Using geometric shapes to calculate irregular shaped areas.

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http://www.brighthubengineering.com/geotechnical-engineering/67792-how-to-measure-the-area-of-land/

The modern way to calculate area is using shapes who's area calculations are known. (LxH - squares, 1/2 base x height - triangles). These shapes are then put inside of the area being calculated. Then all the areas of these shapes area added together in order to find the total area of the land.

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I found out on the Internet that you can overlay a piece of transparent paper on top of the area and then count the number of graphs squares that are positioned over the lake. If the squares are on the edge of the lake, only count the ones where some part of the lake is positioned under at least half the square.

http://www.ehow.com/how_7503862_calculate-size-lake.html

- María

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I found this website: http://www.geog.ucsb.edu/~jeff/115a/lectures/scale_and_area_measurement.html.                                                 To summarize it, the modern way of doing it is taking an aerial picture of the lake and they would spot a building or something like that in the picture. They would take the building's measurement in the picture and take the building measurements in real life and work out the scale. Then they work out the area of the lake on the picture by using methods described here and scaling it up to work out the actual size.

-Jonathon

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I think I read that they used something with different circles which would overlap each other but I did not quite get it. It said that they used this for earthquakes too.

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Oh,... so that's how they do it.
http://www.icsm.gov.au/mapping/surveying2.html

-Mr. Bond

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Fair enough but is that what the good people at Wikipedia have done? Do you believe that that was indeed the method used?

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If we have to calculate the area of an object or a place which has an unknown shape, we can split this shape into different shapes that we know. If we know how to calculate the area of these small shapes, we can calculate them independently and then add them together to find the total area.

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What is your theory based upon. Wouldn't it just be possible to use triangulation and a satellite image?

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Can you share a photo or link? What does that look like? Is this triangulation?

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Online I found that they split up the area into polygons, thus excluding circular areas and finding a best-fit polygon instead, and then putting all the polygons side by side, measure each polygon separately and add them all up. This method is primarily used for countries and borders, but It works on lakes too

-Sergey

link: https://journal.r-project.org/archive/2010-1/RJournal_2010-1_Weidmann+Skrede~Gleditsch.pdf

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My theory is that an organization has set up a bunch of transmitters at each "point" of the lake. The transmitters then detect where the others are and creates a map of the lake that is broken into shapes. They measure how fare they are from each other and use this data to calculate the area of the lake.

Ishaan

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Assuming that you're using triangulation, what would the accuracy of your measures have to be to assure 0.1km^2 results?

-Mr. Bond

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TASK 2 : PLEASE CONTRIBUTE TO THE DISCUSSION

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TASK 2 : PLEASE CONTRIBUTE TO THE DISCUSSION

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Explore the 'real-life' aspects of mapping. The context of the discussion is to find how 'real-life' areas of countries, lakes, etc. are arrived at. According to Wikipedia Zugersee=38.3km2.

What is this value based upon and how could we verify this?