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How to calculate the area of a triangle given 3 line equations ? Watch

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    If you have the equations of 3 lines, how can you calculate the enclosed area without simply drawing a graph?
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    Any examples, I don't quite understand what you mean
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    (Original post by ben167)
    If you have the equations of 3 lines, how can you calculate the enclosed area without simply drawing a graph?
    The GCSE-level way: Solve the equations simultaneously to find where the lines intersect. The three intersection points will be the vertices of the triangle. Then you can find the lengths of the sides using the formula for the length of a line, and then put those lengths into Heron's Formula. Alternatively, you can take one side to be the base, find its corresponding perpendicular height, and then use A=1/2*b*h, but that's a bit more tricky.

    The advanced way: Write the lines in the form
     a_1x+b_1y+c_1=0

a_2x+b_2y+c_2=0

a_3x+b_3y+c_3=0
    Then the area is:
    

\det\begin{bmatrix}a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{bmatrix}^2}
     * 1/(2C_1C_2C_3)
    where C_1,C_2,C_3 are the cofactors of c_1,c_2,c_3 in the above matrix.
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    (Original post by ben167)
    If you have the equations of 3 lines, how can you calculate the enclosed area without simply drawing a graph?
    Find the co-ordinates at which the lines intersect, these will be the vertices of your graph, then use the shoelace method. (Google it).
 
 
 
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