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The area enclosed by the design is calculated as (12)(15)(6 π).

The area enclosed by the design is determined using the formula that incorporates both the dimensions of the basketball court and the circle's characteristics. In this case, the correct calculation results in (12)(15)(6 π).

A) (12)(15)+(6^2)/2 π

This option incorrectly combines the area of a rectangle with an incorrect calculation of the circle's area. The formula used here does not account for the correct dimensions and fails to integrate the circle's area properly, making it an incorrect choice.

B) (12)(15)+6^2π

While this option includes the area of the rectangle, it inaccurately adds the circle's area without proper consideration of the dimensions and the configuration of the design. This leads to an incorrect total area, hence it does not represent the correct answer.

C) (12) (15) + 12 π

In this option, the area of the rectangle is combined with an incorrect circular area calculation. The value of 12 π does not appropriately represent the area of the circle based on the diameter provided, making this choice incorrect.

D) (12) (15) (6 π)

This option correctly applies the formula that combines the rectangle's area with the circle's area, taking into account the proper dimensions and the circle's characteristics. Therefore, this is the correct choice as it accurately computes the area enclosed by the design.

Conclusion

The correct answer, (12)(15)(6 π), effectively calculates the area enclosed by the design by appropriately combining the dimensions of the basketball court and the circle. The other options fail to accurately represent the area due to incorrect formulas or miscalculations, confirming that D is definitively the right choice for this problem.