A triangle has vertices at the points A(2, 3), B(6, 3), and C(4, 7). Determine the area of the triangle. Use the formula for the area of a triangle given by vertices at coordinates $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$:
$$ ext{Area} = rac{1}{2} imes igg| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) igg| $$