If a square of side \(a+b+c\) is split into 3 parts in each direction, how many small sections are formed?

Correct answer: 9

The direct answer is C: nine small sections. A square divided into three parts along one direction has three columns. Dividing it into three parts along the perpendicular direction gives three rows. Every row intersects every column, so the total number of small regions is rows multiplied by columns: \(3\times3=9\). In the identity model, these nine regions correspond to the products formed from \(a,b,c\) on the two sides: three diagonal square regions and six off-diagonal rectangular regions. Option A counts only one direction and therefore gives only three strips, not the complete two-dimensional grid. Option B is not the product of the row and column counts. Option C correctly counts all intersections. Option D has no basis in the stated division. Memory cue: for a rectangular grid, use number of rows times number of columns, not addition.