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The base of a glass paperweight is a regular hexagon with a side length of

6 centimeters. the area of the base is 93.6 square centimeters. the slant height is 12 centimeters. what is the surface area of the paperweight?

User Haxhi
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1 Answer

4 votes

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.

User Rence
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