Area of the triangle using determinant

Math Formulas

Area of the triangle using determinant

Definition and formula description :-
Here we are going to see, how to find the area of a triangle with given vertices using determinant formula.

We know that the area of a triangle whose vertices are (x1, y1),(x2 , y2) and (x3 , y3) is equal to the absolute value of
Area of the triangle using determinant

This expression can be written in the form of a determinant as shown below.Area of the triangle using determinant

Note :
The area of the triangle formed by three points is zero if and only if the three points are collinear.
Also, we remind the reader that the determinant could be negative whereas area is always non negative.

Example 1 :-Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3).

Solution :-
Let the point be Area of the triangle using determinant

Area of the triangle using determinant = (1/2)[3 - 8]
= (1/2)[-5]
= 5/2
= 2.5

Area will not have negative. Hence 2.5 square units is the answer.

Example 2 :-Find the area of a triangle with its vertices located at (-2,2), (1,3) and (3,0)

Solution :-
We plug our coordinates for the vertices into our area formulaArea of the triangle using determinant

And continues withArea of the triangle using determinant Area of the triangle using determinant Area of the triangle using determinant We received a negative value for A and an area cannot be negative, thereforte we must take the absolute value for A:
Area of the triangle using determinant

So the triangle area is 5.5 square units.

Do solve NCERT text book with the help of Entrancei NCERT solutions for class 12 Maths.

Talk to Our counsellor