Area and Perimeter of all type of parallelogram and rhombus

Area and Perimeter of Parallelogram

Area and Perimeter of rhombus

If all the side of a parallelogram touch a circle, show that the parallelogram is a rhombus.OR Prove that a parallelogram circumscribing a circle is a rhombus.

If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side, then the quotient: "Perimeter of rectangle"/"Perimeter of parallelogram" is -

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.