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

You can measure distances the following way.
Stand at one point, say a fence post and face the next fence post. 

Use the ruler to measure:
E:  the distance between your eyes
A: the length of your arm

Now hold the ruler horizontally at arms length so you look past the ruler to see the fence post in the distance.  Close your right eye, and line up the left end of the ruler (the zero point) with the far fence post using your left eye.  Now with out moving, open your right eye and close your left eye.  Read the number of cm from the part of the ruler that lines up with the far fence post using your right eye.  Call that measurement "R".

The Length of this fence, "L", (you were standing at one fence post and looking at the next one) can be determined from:
R/(L-A) = E/L
L = EA/(E-R)

Now you can get the length of all 4 sides.  Also find the length of one of the diagonal.  So now you have 2 triangles.  The area of each triangle can be found from the formula:
A= sqrt((s(s-a)(s-b)(s-c))   where:a,b,c are the lengths of the sides of the triangle.  and s=(a+b+c)/2

Posted by Larry on 2004-12-12 16:49:01