Final answer:
To find the area of the smaller rectangle, you can set up a proportion comparing the areas of the larger and smaller rectangles. Multiply the square root of the area of the larger rectangle by the side length of the smaller rectangle to find the area of the smaller rectangle.
Step-by-step explanation:
To find the area of the smaller rectangle, we need to compare the areas of the larger and smaller rectangles. Since the two rectangles are similar, their areas are proportional.
Let's say the area of the larger rectangle is A and the area of the smaller rectangle is B. The ratio of the areas is given by A:B = (side length of larger rectangle)^2 : (side length of smaller rectangle)^2.
In this case, the area of the larger rectangle is 216 cm². To find the area of the smaller rectangle, we can set up the following proportion:
(side length of larger rectangle)^2 : (side length of smaller rectangle)^2 = 216 : B
Simplifying the proportion, we get (side length of larger rectangle)^2 : (side length of smaller rectangle)^2 = 216 : B
We can solve for B by taking the square root of 216 and multiplying it by the side length of the smaller rectangle:
B = (√216) x (side length of smaller rectangle)
Therefore, the area of the smaller rectangle is (√216)², which is equal to 36 cm².