Question

how to find area of parallogram with 4vertices​

Answer 1

Step-by-step explanation:

For this, we plan to use the Shoelace formula.

Shoelace Formula: Given the coordinates of vertices of a polygon, its area is found by

A=12∣∣∣∑i=1n−1xiyi+1+xny1−∑i=1n−1xi+1yi−x1yn∣∣∣

Or, in other words, we have

A=12|x1y2+x2y3+…xn−1yn+xny1−x2y1−x3y2−…−xnyn−1−x1yn|

Where A is the area of the polygon, and (xi,yi) with i=1,2,3… are the vertices of the polyon

So with your case, the vertices are A(4,2),B(8,4),C(9,6) and D(13,8). We let x1=13,y1=8,x2=9,y2=6,x3=4,y3=2,x4=8,y4=4 and the area is given by

A=12|13⋅6+9⋅2+4⋅4+8⋅8−9⋅8−4⋅6−8⋅2−13⋅4|=12⋅12=6