The cross-sectional areas of the given shapes are 1.0 square inch, 64 square inches, 288 square inches, and 77 square inches respectively. So,
To find the cross-sectional areas of the given shapes:
For the cube with 7-inch edges, the cross section passing through the diagonals of opposite faces would be a square with side length equal to the diagonal of a face. Since the edges are 7 inches long and the diagonal of a face can be found using the Pythagorean theorem, the diagonal is approximately 1.0 inches. The area of a square with side length 1.0 inch is 1.0² = 1.0 square inch.
For the cube with 8-inch edges, a cross section parallel to the base would also be a square with side length equal to the edge length. Therefore, the area of the square would be 8² = 64 square inches.
For the rectangular prism with dimensions 24 inches by 7 inches by 12 inches, a cross section perpendicular to the base and passing through the diagonals would be a rectangle with length 24 inches and width 12 inches (since it passes through the diagonals of the base). Therefore, the area of the rectangle would be 24 * 12 = 288 square inches.
For the rectangular prism with dimensions 3 inches by 7 inches by 11 inches, a cross section parallel to the base would be a rectangle with length 7 inches and width 11 inches (since it is parallel to the base). Therefore, the area of the rectangle would be 7 * 11 = 77 square inches.