A square model has side (c + d). Why will the area calculated from the outer boundary and the area calculated from the inner parts be equal?

Correct answer: Because both describe the area of the same square

The correct answer is A: both calculations describe the area of the same square. From the outside, the square has side c+d, so its area is (c+d)^2. From the inside, the same square is partitioned into smaller regions. Adding the areas of those regions must give the area of the whole figure because the parts fill the square without gaps or overlaps. This is the basic principle behind a visual proof of an algebraic identity. Option A is correct even though the two calculations look different: they measure the same region in two ways. Option B is false because the inner parts are not a separate unrelated figure; they are parts of the original square. Option C confuses perimeter, a boundary length, with area, a measure of surface. Option D is false because the inner parts occupy real space and have nonzero areas. Memory cue: same complete figure, different partition, same total area.