There is one large rectangle ABCD, top line is AD and bottom is BC.

A vertical line is drawn from the top to bottom called GH (between points AD and BC).

A line is drawn from left to right called EF (between points AB and GH).

AEFG is Rectangle 1.
EBHF is Rectangle 2.
GHCD is Rectangle 3.

All three rectangles are similar.

Length of line AE (vertical) is 4cm.
Length of line EB (vertical) is 9cm.

What is the area of rectangle GHCD ?

To find the area of Rectangle 3 (GHCD), we need to make use of the fact that all three rectangles are similar. This means that the corresponding sides of each rectangle are proportional.

First, let's identify the corresponding sides:

- In Rectangle 1 (AEFG), the vertical side AE has a length of 4cm.
- In Rectangle 2 (EBHF), the vertical side EB has a length of 9cm.

Since Rectangle 1 and Rectangle 2 are similar, we can set up the following proportion:

AE / EB = FG / HF

Substituting the given values:

4cm / 9cm = FG / HF

Simplifying the proportion:

4/9 = FG / HF

Now, we can use this proportion to find the length of the vertical side FG in Rectangle 1:

FG = (4/9) * HF

Since Rectangle 3 (GHCD) is similar to Rectangle 1, we can set up the following proportion:

FG / HF = GH / CD

Substituting the previously found value for FG:

(4/9) * HF / HF = GH / CD

Simplifying the proportion:

4/9 = GH / CD

Rearranging the equation, we can solve for GH:

GH = (4/9) * CD

Now, we need to find the length of CD. Since AD and BC are parallel lines, we can use the fact that opposite sides of a rectangle are equal in length. This means that CD is equal to the length of AB.

Since we don't have the value for AB given, we can't directly calculate the area of Rectangle 3.