We can find Area of triangle using formula
base
height if we know the length of base and height of triangle.
We can also find area of triangle using Heron’s formula if we know the length of three sides of triangle.
But, how can we find area of triangle if we know only the coordinates of vertices of triangle. If, we know the vertices of triangle then we can definitely use distance formula to find the length of all the sides which can enable us to use Heron’s formula to find area of triangle. But, this will become too much lengthy and tedious.
We have a formula which can be directly used on the vertices of triangle to find its area.
If, (x1, x2), (x2, y2) and (x3, y3) are the coordinates of vertices of triangle then
Area of Triangle =
Now, we can easily derive this formula using a small diagram shown below.
Suppose, we have a
as shown in the diagram and we want to find its area.
Let the coordinates of vertices are (x1, y1), (x2, y2) and (x3, y3).
We draw perpendiculars AP, BQ and CR to x-axis.
Area of
= Area of Trapezium ABQP + Area of Trapezium BCRQ – Area of Trapezium ACRP
Area of
Example: Find area of triangle whose vertices are (1, 1), (2, 3) and (4, 5)
Solution:
We have (x1, y1) = (1, 1), (x2, y2) = (2, 3) and (x3, y3) = (4, 5)
Using formula:
Area of Triangle =
Because, Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 1 sq units.
Arif says
This formula only works for the 1st quadrant of the coordinate system.
Jashan says
@Arif, this formula works for all 4 quadrants. Take one example and check. You just need to ignore negative sign at the end.
Thanks
HAshim LAwandi TELa says
I am so lucky to have stumbled upon this great website where my Mathematics or rather #Hashematics problems are solved. Thanks alot and God bless!
samuel says
this formular is great
Mads says
im sorry for being too stupid,but what do you mean about (y2 y3). How are we going to solve this one? Is it addition? or multiplication perhaps.
Again, I’m terribly sorry.
Jashan says
y2, y3 are just y values. Example, If in triangle ABC, A =(2,3), B =(10,10) and C = (20,20). Then, we can have x1=2, x2=10 and x3=20. Also, y1=3, y2=10 and y3=20.
yth says
you should use a modulus
Madhu PV says
Excellent, More Excellent, Most Excellent
Madhu says
Excellent, More Excellent, the Most Excellent… Madhu.
Noah Rodriguez (MS172) says
Don’t wrry, I didn’t get it either. can someone explain it in a way a 6th grader could understand cuz im a stupid little kid
Dylan G says
Dang homie, its okay I am a Sophomore in high school who doesn’t get this either.
danish says
this formula is easy to remember
prabhat says
easy formula
Roman says
yes working in all 4 quadrant…..
this is helpful for me..
keep it up