Question

22. Show that the points A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4) are the
vertices of a rhombus. Find the area of this rhombus.​

Answer 1

Properties of Rhombus

1. All sides are equal

2. Diagonal Bisect each other at right angles.

3. Area of Rhombus =  Product of Diagonals

The Vertices of the Given Quadrilateral is A ( 3 , 0 ) , B ( 4 , 5 ) , C ( -1 , 1 ) and D ( -2 , -1 ).

Distance formula between two points  

Now, AB=  

BC=  

As, you can see that , AB≠ BC, Because all sides of rhombus must be equal, so the points A ( 3 , 0 ) , B ( 4 , 5 ) , C ( -1 , 1 ) and D ( -2 , -1 ) are not the vertices of a Rhombus .

As you have asked about ,to find the area of Rhombus.The Polygon which is a Quadrilateral is not a rhombus.