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Bounded Area (Posted on 2004-12-01) Difficulty: 3 of 5
A region of the plane is defined by:
|y-2x| + |y+2x| + |y-3| ≤ 9

What is the area of this region?

See The Solution Submitted by SilverKnight    
Rating: 2.5000 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution (Using Excel) | Comment 2 of 4 |

I plugged the formula into Excel with Y from -2.2 to 4.1 and X from -2.3 to 2.3 and found the same irregular hexagon Charlie found.

http://www.geocities.com/oosterwal/pictures/PERPLEX1.JPG

Rather than finding the area using rectangles and triangles as Charlie did, I found the area with two trapezoids.

The upper trapazoid had bases of lengths of 4 and 4.5 and a height of 1.  The lower trapezoid had bases of 4.5 and 2 with a height of 5.  Plugging the numbers into the H*(b1/2+b2/2) formula I got an area of 20.5

Edited on December 1, 2004, 8:45 pm
  Posted by Erik O. on 2004-12-01 20:25:25

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