Which area partition correctly represents the visual model of a square with side \(a+b\)?

Correct answer: One \(a\times a\) square, one \(b\times b\) square, and two \(a\times b\) rectangles

Correct answer: A. Divide both sides of the square into lengths \(a\) and \(b\). The horizontal and vertical divisions create four regions: one \(a\times a\) square with area \(a^2\), one \(b\times b\) square with area \(b^2\), and two rectangles, each \(a\times b\), with area \(ab\). Thus the total is \(a^2+ab+ab+b^2=a^2+2ab+b^2\). Option B has the wrong number of square regions and gives the wrong total. Option C misses one rectangle, so it gives only one \(ab\). Option D describes triangles rather than the natural rectangular partition; two such triangles would not be the two full cross-rectangles in this model. Memory cue: split both directions, then count 1 large-type square, 1 small-type square, and 2 cross-rectangles.