Maharashtra State BoardHSC Arts 11th
Share

# Area of a Triangle

#### notes

The area of a triangle whose vertices are (x_1, y_1), (x_2, y_2) and (x_3, y_3), is given by the expression  1/2[x_1(y_2-y_3)+ x_2(y_3-y_1)+x_3(y_1-y_2)].
Now this expression can be written in the form of a determinant as ∆ = 1/2 |(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|   ... (1)
Remarks:
(i) Since area is a positive quantity, we always take the absolute value of the determinant in (1).
(ii) If area is given, use both positive and negative values of the determinant for calculation.
(iii) The area of the triangle formed by three collinear points is zero.

#### Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1

Series 2

### Shaalaa.com

Determinants part 19 (Area of triangle using Determinant) [00:05:49]
S
1
0%

S