##### Definition:

A convex quadrilateral is a 4-sided figure in which each vertex relies in the interior of the opposite angle and connects the midpoints of opposite sides. This tutorial explains how to calculate the area of convex quadrilateral for rectangle.

#### Formula:

K =1/4√(2(A^{2}+C^{2})-4X^{2})*(2(B^{2}+D^{2})-4X^{2})sinθ
** Where, **
A,B,C,D = sides
X = distance between the midpoints of the diagonals
Sinθ = the angle between the bimedians
K = Area
##### Example :

A rectangle has four sides A, B, C and D and distance X, where A=5cm,B=6cm,C=10cm,D=8cm, X=7cm distance between the midpoints of the diagonals. Sinθ=60 is the angle between the bimedians.Find the area of convex quadrilateral of the rectangle

##### Given :

A = 5 cm
B = 6 cm
C = 10 cm
D = 8 cm
X = 7 cm
Sinθ = 60 degree

##### To Find :

Area of convex quadrilateral

##### Solution :

Substitute the given values in the formula,

K | =1/4√(2(A^{2}+C^{2})-4X^{2})*(2(B^{2}+D^{2})-4X^{2})sinθ |

| = 1/4 √(2(5^{2}+10^{2})-4*7^{2})(2(6^{2}+8^{2})-4*7^{2})60 |

| =0.03182cm |

##### Result :

Area of convex quadrilateral for rectangle = 0.03182 cm