Question 234479
What is the area of the triangle with vertices (1, 4), (3, 1) and (11, 1)?
<pre><font size = 4 color = "indigo"><b>
The formula for the area of a triangle with vertices

({{{x[1]}}},{{{y[1]}}}), ({{{x[2]}}},{{{y[2]}}}), ({{{x[3]}}},{{{y[3]}}})

is 

{{{A = (1/2)*abs(""abs(matrix(3,3,

x[1], y[1], 1,
x[2], y[2], 1,
x[3], y[3], 1))*"")}}} 

The double bars around the determinant indicate
the absolute value of the determinant:

{{{A = (1/2)*abs(""abs(matrix(3,3,

1, 4, 1,
3, 1, 1,
11, 1, 1))*"")=(1/2)*abs(24) = (1/2)(24) = 12}}}

Just for fun, let's check by drawing the triangle:

{{{drawing(400,200,-1,12,-1,6.5, grid(1),
triangle(1,4,3,1,11,1), line(3,1,11,1),line(3,1,1,4), line(1,4,11,1) )}}} 

Counting the units in the base of the triangle,
we see that the base is 8 units.  Counting the units
in the altitude, or height, of the triangle, we
see that it is 3 units high.  Therefore using the
basic formula for a triangle {{{A=(bh)/2=(8*3)/2=24/2=12}}}.

Edwin</pre>