Learn How to Calculate Area of Convex Quadrilateral for Parallelogram - Formula, Example

Learn How to Calculate Area of Convex Quadrilateral for Parallelogram - Definition

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 parallelogram.

Formula:

K =1/4√(2(A2+C2)-4X2)*(2(B2+D2)-4X2)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 parallelogram 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 parallelogram

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

arc
Solution :

Substitute the given values in the formula,

K =1/4√(2(A2+C2)-4X2)*(2(B2+D2)-4X2)sinθ
= 1/4 √(2(52+102)-4*72)(2(62+82)-4*72)60
=0.03182cm
Result :

Area of convex quadrilateral for parallelogram = 0.03182 cm

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