In the diagram, 18 identical $1 \times 2$ rectangles are put together to form a $6 \times 6$ square. Part of the square is shaded, as shown. What percentage of the area of the $6 \times 6$ square is shaded?
(A) $50 \%$
(B) $67 \%$
(C) $75 \%$
(D) $33 \%$
(E) $25 \%$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-032.jpg?height=415&width=417&top_left_y=1343&top_left_x=1320)
Solution 1

Consider the $6 \times 6$ square as being made up of a $2 \times 6$ rectangle on the left and a $4 \times 6$ rectangle on the right.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-055.jpg?height=455&width=472&top_left_y=1689&top_left_x=881)

Each of these rectangles is divided in half by its diagonal, and so is half shaded. Therefore, $50 \%$ of the total area is shaded.

## Solution 2

The entire $6 \times 6$ square has area $6^{2}=36$.

Both shaded triangles have height 6 (the height of the square).

The bases of the triangles have lengths 2 and 4 :

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-056.jpg?height=445&width=439&top_left_y=409&top_left_x=903)

The left-hand triangle has area $\frac{1}{2} \times 2 \times 6=6$.

The right-hand triangle has area $\frac{1}{2} \times 4 \times 6=12$.

Therefore, the total shaded area is $6+12=18$, which is one-half (or $50 \%$ ) of the area of the entire square.

ANSWER: (A)