In which visual proof is an identity proved by writing the same area in two ways?

Correct answer: Area model

The direct answer is A, the area model. Begin with the key idea: the area of one fixed figure does not change merely because we calculate it in a different way. In an area model, a rectangle or square is divided into smaller parts. We can find the whole area by multiplying its complete length and breadth, or by adding the areas of all the smaller pieces. Because both calculations describe the same figure, the two algebraic expressions must be equal. For example, a square of side a+b has area (a+b)^2. Dividing it into four parts gives a^2+ab+ab+b^2, so (a+b)^2=a^2+2ab+b^2. A is correct because it directly uses equal areas to prove an identity. B represents positions and distances on a line, not usually a partitioned-area proof. C may show time relationships but is not the standard model here. D organizes values in rows and columns but does not itself show that two expressions represent the same geometric area. Memory cue: same shape, same area, two calculations means an area proof.