Question

Dara is constructing a plant stand using a cube and a rectangular prism. She intends to stain all sides of both pieces of the plant stand, except for the bottom of the larger prism. Calculate the surface area of the part of the plant stand she will stain.

Answer 1

To calculate the surface area of the part of the plant stand that Dara will stain, we need to find the surface area of the cube and the rectangular prism. The total surface area that Dara will stain is 6s^2 + 2lh + 2wh.

Step-by-step explanation:

To calculate the surface area of the part of the plant stand that Dara will stain, we need to find the surface area of the cube and the rectangular prism.

The surface area of a cube with side length s is given by the formula 6s^2.

The surface area of a rectangular prism with length l, width w, and height h is given by the formula 2lw + 2lh + 2wh.

In this case, Dara will stain all sides of both pieces except for the bottom of the larger prism. So we need to subtract the area of the bottom face of the larger prism from the total surface area.

Let's assume the side length of the cube is s and the dimensions of the rectangular prism are l, w, and h.

The total surface area that Dara will stain is 6s^2 + 2lw + 2lh + 2wh - lw = 6s^2 + 2lh + 2wh.