# Express the area of a triangle given by vertices, #A(x_1,y_1), B(x_2,y_2), C(x_3,y_3)#. Show that it can be expressed as determinant of: #det(Delta) = [(1, 1, 1 ),(x_1, x_2, x_3),(y_1, y_2, y_3) ]#.Calculate the area of A(3,6), B(7,8), & C(5,2)?

##### 1 Answer

Sep 24, 2016

See below.

#### Explanation:

The triangle area can be computed as a closed circuit integral. So

Expanding and simplifying

For the example given we have

Of course this must be considered in absolute value. So