Answer:
The surface area of a solid object like a paperweight is calculated by adding the areas of all its faces. In this case, the paperweight is like a hexagonal pyramid, with a hexagonal base and six triangular sides. The base area has already been given as 93.6 square centimeters.
The six triangles are isosceles triangles, since the base of each triangle is a side of the hexagon, and the slant height is the same for each triangle.
The area of an isosceles triangle is given by the formula:
Area = 1/2 * base * height
For these triangles, the base is 6 cm (side length of the hexagon), and the height is the slant height, which is 12 cm.
So the area of one triangle is:
Area = 1/2 * 6 cm * 12 cm = 36 square cm
Since there are six such triangles, the total area of the triangular faces is:
6 * 36 square cm = 216 square cm
So, the total surface area of the paperweight is the area of the base plus the area of the six triangular faces, or:
93.6 square cm (base) + 216 square cm (sides) = 309.6 square cm
So the surface area of the paperweight is 309.6 square cm.