The Area of a Triangle Using a Determinant

​
A =
1
2

-7.21
-5.31
1
4.12
0.23
1
-2.27
2.85
1
 = 32.5426
The area of a triangle with vertices at the coordinates
(a,b)
,
(c,d)
, and
(e,f)
is the absolute value of
A=
1
2

a
b
1
c
d
1
e
f
1

.

Details

For how to calculate a 3×3 determinant, see the first two related links.

External Links

3×3 Determinants Using Diagonals
3×3 Determinants by Expansion
Triangle Area (Wolfram MathWorld)

Permanent Citation

George Beck
​
​"The Area of a Triangle Using a Determinant"​
​http://demonstrations.wolfram.com/TheAreaOfATriangleUsingADeterminant/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011