96cm². The are of the rhombus of the image is 96cm².
The key to solve this exercise is breaking down the rhombus in four equals right triangles, each triangle has the sides 10cm, 8cm and 6cm. We can calculate the area of one right triangle and multiply by 4 in order to get the total area of the rhombus.
The area of a triangle is where b is the base and h is the height.
The base of the one right triangle is 8cm and the height is the leg adyacent to the right angle that is 6cm. Calculating the area of the right triangle:
The ratio of the smaller to the larger is given as 2:4. Another way to write this is as a fraction: which of course you can see now will reduce to . That's your ratio.