Square $A B C D$ is divided into four identical smaller squares, which are further divided into triangles, as shown. What fraction of $A B C D$ is shaded?
(A) $\frac{1}{4}$
(B) $\frac{15}{32}$
(C) $\frac{7}{16}$
(D) $\frac{3}{8}$
(E) $\frac{7}{8}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-010.jpg?height=377&width=414&top_left_y=256&top_left_x=1300)
We begin by constructing the three diagonals inside the smaller squares that were missing from the diagram given in the question, as shown.

The two diagonals inside each of these 4 smaller squares divide each smaller square into 4 identical triangles having equal area. Thus, square $A B C D$ is divided into $4 \times 4=16$ such triangles. Since 7 of these triangles are shaded, then the fraction of $A B C D$ that is shaded is $\frac{7}{16}$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-028.jpg?height=384&width=412&top_left_y=1868&top_left_x=1518)

ANSWER: (C)

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