Final answer:
The area of triangle ABC is 6.5 square units.
Step-by-step explanation:
To find the area of the triangle ABC, we can use the Shoelace Formula. First, we label the vertices A(5,4), B(5,1), and C(3,2). Next, we calculate the sum of the products of the coordinates of each vertex and the coordinates of the next vertex in counterclockwise order. Subtracting the sum of the products going in clockwise order, we take the absolute value of the result and divide by 2 to find the area:
|(5*1 + 1*3 + 3*4) - (4*5 + 3*1 + 5*2)| / 2 = |(5 + 3 + 12) - (20 + 3 + 10)| / 2
= |20 - 33| / 2 = 13 / 2
= 6.5 square units.