Okay, let's solve this step-by-step:
1) The two parallelograms are similar. This means they have the same shape and proportions, but different sizes.
2) The area of the larger parallelogram is 288cm2.
3) To find the area of the smaller parallelogram, we need to know the ratio of their sizes. Since they are similar, we can use any two corresponding sides.
4) Let's call the lengths of the sides of the larger parallelogram: a, b
And the lengths of the sides of the smaller parallelogram: x, y
5) Setting up the ratio: a/x = b/y (since they are similar triangles)
6) We know: a = ? (the length of any side of the larger parallelogram) And a/x = ? (the size ratio we need to find the area)
7) Now we also know: The area of the larger parallelogram = 288cm2
=> a * b = 24cm
8) Substitute in the ratio: a/x = 24/x
=> x = 4 (solve for x)
9) Now we know:
The size ratio is a/x = 24/4 = 6
And the area ratio is (a*b)/(x*y) = 6^2 = 36
10) Therefore, the area of the smaller parallelogram = 288/36 = 8cm^2
Does this make sense? Let me know if you have any other questions!