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 Grass Roots (Posted on 2004-12-12)

You have been captured by a mad king, he has placed you in a large field, he says you are free to go once you have calculated the area of the field.

He has left you with 1 pencil, 1 piece of paper, and 1 30cm ruler.

What is the quickest way to work out the area of the field, so you can go home to your family?

NOTE, from any position inside the field you can see the entire perimeter, assume that the field has four straight sides, though the angles may all be different.

Also, the area of the field is large enough to make it impractical to measure with the ruler

 Submitted by Juggler Rating: 4.5000 (2 votes) Solution: (Hide) Go to roughly the middle of the field, then place a dot in the middle of your piece of paper, ensure you keep the paper in exactly the same orientation always, then draw lines outwards from this dot towards all the corners of the field, it doesn't matter how many there are you need to do them all. then move to a second point in the field (try to move parallel to one fence) you will need to measure this distance later so consider marking both points with an item of clothing. repeat the first step again, orientate your paper in exactly the same way as before, add a dot to your paper to represent your second position and draw lines out to the corners of the field, you should now have a series of crossed lines with two dots on your paper, connect the intersections of the dots, this is now the correct shape of the field, measure the distance between the 2 dots, and do the same on the ground, this will give you a ratio of the field size, calculate the area of the small drawing, then multiply by the ratio. Then go home for tea.

 Subject Author Date re(2): the author's solution Hugo 2004-12-17 20:23:13 re: the author's solution Larry 2004-12-17 16:52:13 re(3): REAL SOLUTION Larry 2004-12-17 16:47:22 re(2): REAL SOLUTION Timothy Bard 2004-12-14 18:03:53 practial solution Andrea 2004-12-14 00:04:46 re(3): Solution Juggler 2004-12-13 09:37:05 re(2): Solution Larry 2004-12-13 00:36:04 re: Solution Juggler 2004-12-12 23:23:44 re: REAL SOLUTION Larry 2004-12-12 20:39:15 REAL SOLUTION Steven Lu 2004-12-12 20:31:26 Alternate method Charlie 2004-12-12 19:27:38 re: Solution Charlie 2004-12-12 19:01:27 Solution Larry 2004-12-12 16:49:01

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