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Geometry: 3-D Measurements

Problems

Surface Area

Volume

Problem : Does a polygon have surface area?

Yes, it does. A polygon is two-dimensional, so it has area. And polygons are surfaces. We don't call the area of a polygon its surface area because a polygon is a region in a plane, and, as a surface, it only spans two dimensions. Area is sufficient to describe the measurement of its combined length and width. But yes, it is correct to say that a polygon has surface area. (The surface area of a polyhedron is only the sum of the area of polygons!)

Problem : What is a shortcut for calculating the surface area of a regular polyhedron?

The surface area of a regular polyhedron is n times the area of one face, where n is the number of sides that polyhedron has.

Problem : The area of a circle is 4Π . What is the surface area of the sphere with the same radius?

16Π

Problem : What is the surface area of a cube with edge length 4 inches?

96 square inches

Problem : Does surface area change with respect to the concavity of a polyhedron?

No. Only the size of a surface matters for surface area. The direction of the surface has no bearing on surface area.

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