The base of a right prism is a triangle with sides of 12 cm, 16 cm, and 20 cm. If the height of the prism is 9 cm, the surface area of the prism is  .a bc d

To find the surface area of a right prism, we need to calculate the area of the base, the area of the sides (also known as the lateral area), and then add those together.

Step 1: Calculate the area of the base The base of the prism is a triangle. Since the sides of the triangle are 12 cm, 16 cm, and 20 cm, this is a right triangle (because 20^2 = 12^2 + 16^2). The area of a right triangle is given by the formula 1/2 * base * height. Here, we can take 12 cm and 16 cm as the base and height (it doesn't matter which one is the base and which one is the height). So, the area of the base is 1/2 * 12 cm * 16 cm = 96 cm^2.

Step 2: Calculate the lateral area The lateral area of a prism is the perimeter of the base times the height of the prism. The perimeter of the base (the triangle) is 12 cm + 16 cm + 20 cm = 48 cm. The height of the prism is given as 9 cm. So, the lateral area is 48 cm * 9 cm = 432 cm^2.

Step 3: Add the areas together The total surface area of the prism is the area of the base plus the lateral area. So, the surface area is 96 cm^2 (base area) + 432 cm^2 (lateral area) = 528 cm^2.