Area Of Quadrilateral
The area of the quadrilateral formed by the points (2, 9), (4, 5), (6, 9) and (–2, 5) is? I had a formula for calulating the area. 2*Area = (x1y2-x2y1) + (x2y3-x3y2) + (x3y4-x4y3) + (x4y1-x1y4) But, is there any other simple way for solving this? Thanks in advance.
As such this is the simplest
As such this is the simplest method but some times you might get 4 points which form a rectangle and square or some thing similar.
So the trick is to figure out if the four points are the co-ordinates of any such figure and in that case you can mentally calculate the area without using the formula.
Area of the Quadrilateral.
Hi,
Good is the case if we can visualise that co-ordinates are forming regular structures like rectangle or square. But, What about this case?
Since, it is quadrilateral, is it that we don't have any other solution than working it out with the help of the formula.
Thank you.
I would also like to know if
I would also like to know if any such solution exists.
Any guru out there
Sorry to disappoint you all
Sorry to disappoint you all but I don’t think there is any other formula.
What else you can do is calculate the length of the sides/perpendiculars and use the below formula
Area= 1/2 (pqsin θ)
= 1/4(b2 +c 2 -a2 - d2)tanθ
Where p, q, a, b and etc are as shown in the below diagram.
(Note : please don’t use the above formula for CAT purpose)
I have a solution
see u have 4 co-ordinates.I hope u have an idea of calculating area of triangle using determinants process.for a triangle find det of (x1,y1),(x2,y2),(x3,y3).keep the co-ordinates in column manner.
x1 x2 x3 x1
y1 y2 y3 y1
multiply (x1*y2-x2*y1)+(x2*y3-y2*x3)+(x3*y1-x1*y3)
find the ans and divide by 2
this can be applied to a quadrilateral also.