A rhombus and a square have one and the same side of 6 cm. The area of the rhombus is 4/5 of the area of the square. Find the height of the rhombus.

Answer: The area of the rhombus is 9.6 cm.

To start, we can find the area of the square. 6 x 6 = 36 cm^2

Since the area of the rhombus is 4/5 of the area of the square, we multiply 36 by 0.8 = 28.8 cm^2 is the area of the rhombus.

Now, use the area formula for a rhombus to find the height of the rhombus.

A = 0.5bh

28.8 = 0.5 (6) h

9.6 = h