**I. Polyhedra**. A **polyhedron **is a three-dimensional figure whose surfaces are polygons. Each polygon is
a **face **of the polyhedron. An **edge **is a segment that is formed by the intersection of two faces.
A **vertex **is a point where three or more edges intersect.

**II. Nets**. Use each net to find a formula for the surface area of the polyhedron.

1. Find a formula for the surface area of a cube with side length *s*.

2. Find a formula for the surface area of a cylinder with radius *r* and height *h*.

3. Find a formula for the surface area of a cone with radius *r*, height *h*, and slant height *l*.

4. Find a formula for the surface area of the square pyramid pictured above.

**III. Prisms**. A **prism **is a polyhedron with exactly two congruent, parallel faces, called **bases**.
The other faces are called **lateral faces**. You name a prism by the shape of its base.
An altitude of a prism is a perpendicular segment that joins the planes of the bases.
The height of the prism is the length of an altitude.

5. Find a formula for the surface area of a rectangular prism with height *h*, length *l*, and width *w*.

6. Use the slider to change the height, length, and width of the rectangular prism and caluclate the surface area.
Use the slider on the right to check your answer.

7. Find a formula for the surface area of the right triangular prism pictured above.

8. Use the slider to change the dimensions of the right triangular prism and calculate the surface area.
Use the slider on the right to check your answer.

9. Find a formula for the surface area of the triangular prism pictured above.

10. Use the slider to change the dimensions of the triangular prism and calculate the surface area.
Use the slider on the right to check your answer.

**IV. Pyramids**. A **pyramid **is a polyhedron in which one face (the base) can be any polygon and the other face
(the **lateral faces**) are triangles that meet at a common vertex. You can name a pyramid by the shape of its base.
The altitude of a pryramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height of the pyramid.
A **regular pyramid** is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.

11. Find a formula for the surface area of a rectangular pyramid with height *h*, length *l*, width *w*, and slant
height *s.h.*.

12. Use the slider to change the height, length, and width of the rectangular pyramid and caluclate the surface area.
Use the slider on the right to check your answer.