Which of these shapes requires the use of the diagonals in its area formula?

The area formula for a rhombus specifically incorporates the lengths of the diagonals. In a rhombus, the diagonals are not only significant for defining the shape but also crucial for calculating its area. The formula for the area of a rhombus is given by ( \text{Area} = \frac{1}{2} \times d_1 \times d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals.

While the other shapes listed—parallelogram, rectangle, and square—do have area formulas, they do not involve diagonals in their calculations. For instance, the area of a rectangle and a square is determined by multiplying the lengths of their sides, while the area of a parallelogram is calculated using the base and height. Therefore, using the lengths of the diagonals is specifically a requirement for determining the area of a rhombus.