﻿ Surface Area - GeoGebra Dynamic Worksheet

## Investigating Surface Area

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.

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GeoGebra Applet pictured above: ch11_polyhedron.ggb.

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

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GeoGebra Applet pictured above: ch11_netcube.ggb.

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

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GeoGebra Applet pictured above: ch11_netcylinder.ggb.

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

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GeoGebra Applet pictured above: ch11_netcone.ggb.

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

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GeoGebra Applet pictured above: ch11_netPyramid.ggb.

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.

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GeoGebra Applet pictured above: ch11_rectangularPrism.ggb.

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.

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GeoGebra Applet pictured above: ch11_triangularPrism.ggb.

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.

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GeoGebra Applet pictured above: ch11_triangularPrism2.ggb.

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.

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GeoGebra Applet pictured above: ch11_rectangularPyramid.ggb.

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.