# Calculate the area of a triangle with vertices (1,1),(3,1) and (5,7).

Given, the vertices of triangle are (1,1),(3,1) and (5,7).

By the formula of area of triangle when coordinates of vertices are given, we have;

$\frac{1}{2}\left|\mathbf{x}_{1}\left(\mathbf{y}_{2}-\mathbf{y}_{3}\right)+\mathbf{x}_{2}\left(\mathbf{y}_{3}-\mathbf{y}_{1}\right)+\mathbf{x}_{3}\left(\mathbf{y}_{1}-\mathbf{y}_{2}\right)\right|$

Therefore,

Area of triangle with vertices (1,1),(3,1) and (5,7), we get;

Area = 1/2 [1(21−5)−1(7−5)+1(1−3)]

= 1/2 [16 – 2 – 2]

= 6 sq.unit.