Q: What is the name of sum of the areas of all faces of a solid figure?

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a triangular prism.

triangular prism

Well, a triangular prism has 5 faces and 6 vertices, but it has 9 edges. So I'm not sure.

square-based pyramid

A cube has six square faces.

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A cone

triangular prism

a triangular prism.

A pyramid

a cylinder a cylinder

A hexahedron is a solid with six plane faces, and a cuboid is a six-sided figure each face of which is a rectangle.

A triangular pyramid.

triangular prism

Well, a triangular prism has 5 faces and 6 vertices, but it has 9 edges. So I'm not sure.

Lots of them. A cuboid, a cylinder, a prism, a regular dodecahedron, a frustum of a cone, a parallelepiped to name a few.

square-based pyramid

A pyramid with a square base is called a pentahedron. This is because it is a solid figure that has five faces, and each one of its faces can be turned by 120 degrees.