Answer:
[tex]\boxed{Area=19.5units^2}[/tex]
Step-by-step explanation:
A triangle is any polygon with exactly 3 sides. Let's call this sides the vertices of the triangle, and let's say:
[tex](7,1)=A(7,1) \\ \\ (0,10)=B(0,10) \\ \\ (9,4)=C(9,4)[/tex]
Where:
[tex]A=(A_{x},A_{y}) \\ B=(B_{x},B_{y}) \\ C=(C_{x},C_{y})[/tex]
A formula for finding the area of a triangle given its vertices is:
[tex]Area=|\frac{A_{x}(B_{y}-C_{y})+B_{x}(C_{y}-A_{y})+C_{x}(A_{y}-B_{y})}{2}| \\ \\ Area=|\frac{7(10-4)+0(4-1)+9(1-10)}{2}| \\ \\ Area=|\frac{-39}{2}| \\ \\ \boxed{Area=19.5units^2}[/tex]
Finally, the area of the triangle defined by the coordinates (7,1), (0,10), and (9,4), to the nearest tenth is 19.5 squared units.
