Question

if the vertices of the triangle are colliner . Then what is the area of the triangle

Answer 1

If the vertices of a triangle are collinear, then the area is none other than 0 unit².

Let two sides of a triangle be 'a' and 'b'. Since the vertices are collinear, the third side, the largest side, say 'c', will be the sum of the other two sides, i.e., 'c = a + b'.

[To check whether it's true, you can use Law of Cosines]

So the semiperimeter will be,

s = (a + b + a + b) / 2 = a + b = c

We can find the area by using Heron's Formula.

In this formula, we can see that (s - c) is multiplied within the square root. Since both are same, it'll be 0. Hence the area of the triangle.

That's all!