The area model of a square with side \(t+1\) leads to which result?

Correct answer: \(t^2+2t+1\)

Direct answer: option D, \(t^2+2t+1\). The area of a square is the square of its side, so the total area is \((t+1)^2\). In the visual model, split both sides into lengths \(t\) and 1. The four pieces are a \(t\) by \(t\) square with area \(t^2\), two \(t\) by 1 rectangles with total area \(t+t=2t\), and a 1 by 1 square with area 1. Thus the total is \(t^2+2t+1\). This is the identity \((a+b)^2=a^2+2ab+b^2\). Option A omits both middle rectangles. Option B has a negative middle term, which belongs to a difference such as \((t-1)^2\). Option C uses the wrong coefficient for the middle term; two rectangles give 2t, not 3t. Memory cue: square, two equal rectangles, square gives \(t^2+2t+1\).