Final answer:
The surface area of the right rectangular pyramid is 177 square units.
Step-by-step explanation:
A right rectangular pyramid has a rectangular base and triangular sides that meet at a common vertex.
To find the surface area of the pyramid, we need to calculate the area of the base and the area of the four triangular faces.
The area of the base is equal to the length multiplied by the width, which is W * X = 5 * 12 = 60 square units.
The area of each triangular face can be calculated using the formula base * height / 2.
So, the total area of the four triangular faces is (W * Y + X * Y + W * Z + X * Z) / 2 = (5 * 9 + 12 * 9 + 5 * 6 + 12 * 6) / 2 = 117 square units.
Adding the base area and the area of the four triangular faces, we get the total surface area of the right rectangular pyramid: 60 + 117 = 177 square units.