Find area of triangle whose vertices are (1, 1), (2, 3) and (4, 5)

Step 1: Locate the coordinates of the endpoints.
The given points M (1, 1) and N (2, 3), (4, 5)
Therefore, (x_1, y_1) = (1, 1), (x_2, y_2) = (2, 3) and (x_3, y_3) = (4, 5).
Step 2: Set up triangle area formula when vertices are given.
FORMULA: Area of the triangle
\frac{1}{2} {x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}
Step 3: Plug the corresponding coordinates into the Area of triangle formula.
= \frac{1}{2} {x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}
= \frac{1}{2} (1*[3 - 5] + (2)*[5 - 1] + 4*[1 - 3])
Step 4: Simplify further
NOTE: Apply the BODMAS rules
= \frac{1}{2} (1*[-2] + (2)*[4] + 2*[-2])
= \frac{1}{2} (- 2 + 8 - 4)
= \frac{1}{2} (8 - 6])
= \frac{1}{2} (2)
= 1
Hence, area of the triangle = 1 units