A rectangle has length \(r+s\) and breadth \(r\). What will be the total area in the area model?

Correct answer: \(r^2+rs\)

Direct answer: option A, \(r^2+rs\). The area of a rectangle is length multiplied by breadth. Split the length \(r+s\) into two parts, \(r\) and \(s\), while keeping the breadth \(r\). The first smaller rectangle has dimensions \(r\) by \(r\), so its area is \(r^2\). The second has dimensions \(s\) by \(r\), so its area is \(rs\). Adding the two non-overlapping areas gives \(r^2+rs\). Equivalently, the distributive law gives \(r(r+s)=r\cdot r+r\cdot s=r^2+rs\). Option B incorrectly uses \(s^2\), which would require a square with side \(s\). Option C doubles the product and does not represent the given rectangle. Option D is only the length, not an area. Memory cue: multiply the unchanged breadth by each split part: \(r\cdot r+r\cdot s\).