In the visual model of a square with side \(a+b\), which statement is correct?

Correct answer: The square is divided into four parts: one \(a^2\) square, one \(b^2\) square, and two \(ab\) rectangles.

The correct answer is A. Divide each side of the large square, whose side is \(a+b\), into parts of lengths \(a\) and \(b\). The resulting grid has four regions: an \(a\)-by-\(a\) square with area \(a^2\), an \(a\)-by-\(b\) rectangle with area \(ab\), a second equal \(b\)-by-\(a\) rectangle with area \(ab\), and a \(b\)-by-\(b\) square with area \(b^2\). Thus the total area is \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option B leaves out both cross-rectangles and therefore gives too little area. Option C has no basis in the side lengths and does not describe the four regions. Option D mentions the two rectangles but ignores the two square regions, so it is incomplete. The important visual habit is to count every region created by dividing both directions into \(a\) and \(b\).