Using Determinants to Find Area
Date: 06/09/98 at 20:52:31 From: Darren Goldner Subject: Finding the area of triangles and parallelograms through the use of determinants I'm a high school mathematics student at Stuyvesant in New York City. My math teacher has assigned me the task of reporting upon how the area of a triangle and that of a parallelogram can be found through the use of determinants. I have no idea where to start. Can you give me the formulae and explanations? Thank you for your attention.
Date: 06/09/98 at 23:35:51 From: Doctor Pat Subject: Re: Finding the area of triangles and parallelograms through the use of determinants Darren, If the triangle or parallelogram is in the coordinate plane you can find the area using just the three vertices of the triangle (or three adjacent vertices of the parallelogram) in a 3x3 matrix. For the points (xa,ya), (xb,yb), (xc,yc), you can just put the x and y values in as the first two rows of the matrix, then fill the third row with ones: | xa xb xc | | ya yb yc | | 1 1 1 | The absolute value of the determinant is the area of the parallelogram, and 1/2 that value is the area of the triangle. There is also a way to do this with vectors that involves what is called the cross product. If you have the desire to pursue more ways to do this, why not use the search engine here at the Math Forum to search for key words like "vector cross product"? The searcher is at http://mathforum.org/grepform.html There are lots of interesting ideas in math that a knowledge of vectors can help you to understand. Good luck, -Doctor Pat, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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