Answer:
13 sq. units.
Step-by-step explanation:
We have to calculate the area of the triangle whose vertices are (4,1), (1,5) and (6,7).
We know that the area of a triangle with vertices [tex](x_{1},y_{1})[/tex], [tex](x_{2},y_{2})[/tex], and [tex](x_{3},y_{3})[/tex] is given by the formula
[tex]\frac{1}{2} |x_{1}(y_{2} - y_{3}) + x_{2}(y_{3} - y_{1}) + x_{3}(y_{1} - y_{2})|[/tex]
So, the area of the given triangle will be
= [tex]\frac{1}{2}|4(5 - 7) + 1(7 - 1) + 6(1 - 5)| = 13[/tex] sq. units. (Answer)
