How to get size of a rotated rectangle [duplicate]

Answer 1

Calculate the area of the original rectangle. Area doesn't change under rotation.

Answer 2

For the axis aligned box of the rotated rectangle, you find the minimum and maximum of each of the 4 rotated coordintates. The minX and minY becomes 1 corner and the maxX and maxY becomes the other corner.

Answer 3

To construct an axis-aligned bounding box, one must find the extreme points of the rotated box. i.e.,

given a rectangle 'P', given by points P1=(0,0), P2=(x,0), P3(x,y), P4(0,y), rotated 'R' degrees; find minX, maxX, minY, maxY, such that the box [(minX,minY),(maxX,maxY)] completely bounds the rotated 'P'.

                          +-------P3'----+maxY
                          |     /    \   |
  P4------P3              |   /        \ |
   |      |    rotate     | /            P2'
   |      | => by 'R' =>  P4'           /|
   |      |    degrees    | \         /  |
  P1------P2              |   \     /    |
                          |     \ /      |
                          +-----P1'------+minY
                         minX           maxX

The values for the bounding box are the minimum/maximum of the components of the rotated points P1'..P4'; thus,

minX=min(P1'[x],P2'[x],P3'[x],P4'[x])
maxX=max(P1'[x],P2'[x],P3'[x],P4'[x])
minY=min(P1'[y],P2'[y],P3'[y],P4'[y])
maxY=max(P1'[y],P2'[y],P3'[y],P4'[y])

For a discussion of 2D rotations, see http://en.wikipedia.org/wiki/Transformation_matrix#Rotation

Answer 4

a = abs(x * sin(o)) + abs(y * cos(o))
b = abs(x * cos(o)) + abs(y * sin(o))

Answer 5

Use [Heron's Formula Triangle Area Calculator] s = (a + b + c) / 2 or 1/2 of the perimeter of the triangle

A = SquareRoot(s * (s - a) * (s - b) * (s - c))

Where

a=SquareRoot((X1-X2)^2+(Y1-Y2)^2)  [Side 1 Length]
b=SquareRoot((X1-X3)^2+(Y1-Y3)^2)  [Side 2 Length]
c=SquareRoot((X2-X3)^2+(Y2-Y3)^2)  [Side 3 Length]

X1,Y1,X2,Y2,X3,Y3 are the coordinations of any three points (Corners)

RectangleArea=2*A

Or Direct without [Heron's Formula Triangle Area Calculator], sequence of points are important here.

P1----P2
|     |
P3----P4

 a=SquareRoot((X1-X2)^2+(Y1-Y2)^2)  [Side 1 Length]
 b=SquareRoot((X1-X3)^2+(Y1-Y3)^2)  [Side 2 Length]
 RectangleArea=a*b

Answer 6

It's a bit complicated, but for a rectangle, Area = b * h = length * width.