$A B C D$ is a square that is made up of two identical rectangles and two squares of area $4 \mathrm{~cm}^{2}$ and 16 $\mathrm{cm}^{2}$. What is the area, in $\mathrm{cm}^{2}$, of the square $A B C D$ ?
(A) 64
(B) 49
(C) 25
(D) 36
(E) 20
$A B C D$ is a square that is made up of two identical rectangles and two squares of area $4 \mathrm{~cm}^{2}$ and 16 $\mathrm{cm}^{2}$. What is the area, in $\mathrm{cm}^{2}$, of the square $A B C D$ ?
(A) 64
(B) 49
(C) 25
(D) 36
(E) 20

## Solution

One way to draw the required square is shown in the diagram. The smaller square has a side length of $2 \mathrm{~cm}$ and the larger a side length of $4 \mathrm{~cm}$. This gives the side length of the larger square to be $6 \mathrm{~cm}$ and an area of $36 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-421.jpg?height=372&width=398&top_left_y=1397&top_left_x=1338)

Note that it is also possible to divide the square up as follows:

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-421.jpg?height=369&width=415&top_left_y=1832&top_left_x=1321)

ANSWER: (D)