In a rectangle model, the length is (x+6) and the breadth is (x-2). What is the total area after adding the parts?

(x^2+4x-12)

The rectangle’s area is the product of its length and breadth: \\( (x+6)(x-2)\\). Multiplying each part gives \\(x\cdot x=x^2\\), \\(x\cdot(-2)=-2x\\), \\(6\cdot x=6x\\), and \\(6\cdot(-2)=-12\\). Combining like terms gives \\(x^2-2x+6x-12=x^2+4x-12\\). In a signed visual model, the negative width creates negative regions, so their signs must be retained when areas are combined algebraically.

Therefore option A is correct. The middle terms combine to \\(4x\\), and the constant corner is negative \\(-12\\). Option B incorrectly adds the two x-products as if both were positive. Option C reverses the signs of the middle and constant terms, while option D treats the constant product as positive. Careful distribution and sign handling lead directly to the stated total area.

This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.