The area of quadrilateral can be found by splitting it into two triangles and ading up their areas.
The area of the quadrilateral whose vertices taken in order are A(x_{1}, y_{1}), B(x_{2}, y_{2}), C(x_{3}, y_{3}), D(x_{4}, y_{4}).
Write down the coordinates as shown
Area of Quad ABCD = Area of triangle ABC + Area of triangle ACD
= 1/2{(x_{1}y_{2})(x_{2}y_{1}+(x_{2}y_{3}x_{3}y_{2}(x_{3}y_{1}x_{1}y_{3})} + 1/2{(x_{1}y_{3}x_{3}y_{1})+x_{3}y_{4}x_{4}y_{3})+ (x_{4}y_{1}x_{1}y_{4}}
=1/2[(x_{1}y_{2}x_{2}y_{1})+(x_{2}y_{3}x_{3}y_{2})+(x_{3}y_{4}x_{4}y_{3})+(x_{4}y_{1}x_{1}y_{4})]
Example: Find the area of the quadrilateral whose vertices are (3.4), (0,5),(2,1) and (3,2).
The required area is
1/2[3x50x4+0x(1)5x2+2x(2)(1)(3)+3x4(2)(3)]
Answer: 11 sq.units
Directions: Solve the following.
