You should use the following formula to evaluate the area of triangle such that:

`S = (1/2)|[(x_A,y_A,1),(x_B,y_B,1),(x_C,y_C,1)]|`

You should substitute the values of coordinates of vertices such that:

`S = (1/2)|[(4,-3,1),(4,1,1),(2,1,1)]|` = `(1/2)|(4 + 4 - 6 - 2 - 4 + 12)|`

`S = 8/2 => S = 4`

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You should use the following formula to evaluate the area of triangle such that:

`S = (1/2)|[(x_A,y_A,1),(x_B,y_B,1),(x_C,y_C,1)]|`

You should substitute the values of coordinates of vertices such that:

`S = (1/2)|[(4,-3,1),(4,1,1),(2,1,1)]|` = `(1/2)|(4 + 4 - 6 - 2 - 4 + 12)|`

`S = 8/2 => S = 4`

You may also use Heron's formula to evaluate the area of triangle but you should find the lengths of sides of triangle such that:

`a = sqrt((x_C - x_B)^2+(y_C - y_B)^2)`

`a = sqrt((2-4)^2 + (1-1)^2) => a = 2`

`b = sqrt((x_C - x_A)^2+(y_C - y_A)^2)`

`b = sqrt((2-4)^2+(1+3)^2) => b = sqrt20 = 2sqrt5`

`c = sqrt((x_B - x_A)^2 + (y_B-y_A)^2)`

`c = sqrt((4-4)^2 + (1+3)^2) => c = 4`

Hence, using the Heron's formula yields:

`S = (1/4)sqrt((a+b+c)(a+b-c)(a+c-b)(b+c-a))`

`S= (1/4)sqrt((6+2sqrt5)(2sqrt5 - 2)(6-2sqrt5)(2sqrt5+ 2))`

`S= (1/4)sqrt((6^2 - (2sqrt5)^2)((2sqrt5)^2 - 2^2))`

`S = (1/4)sqrt((36 - 20)(20 - 4)) => S = (1/4)sqrt(16*16)`

`S = 16/4 => S = 4`

**Hence, evaluating the area of triangle, under the given conditions, yields `S = 4` .**