The surface area of a pyramid is the total area of all its faces. This includes the area of the base and the area of all the lateral faces (the triangular faces). To calculate it, you need to find the area of each face and then add them together. For a regular pyramid, where all the lateral faces are congruent triangles, you can use the formula: Surface Area = Area of Base + (Number of Lateral Faces * Area of One Lateral Face).
Understanding the difference between the slant height and the actual height of the pyramid is also crucial. The slant height is the height of a lateral face, while the height of the pyramid is the perpendicular distance from the apex to the base.
Match the term to its definition:
| Term | Definition |
|---|---|
| 1. Apex | A. The height of a lateral face of the pyramid. |
| 2. Base | B. The sum of the areas of all the faces of the pyramid. |
| 3. Slant Height | C. The point on the pyramid opposite the base. |
| 4. Lateral Face | D. A triangular face of the pyramid, excluding the base. |
| 5. Surface Area | E. The polygon at the bottom of the pyramid. |
A pyramid is a three-dimensional shape with a polygonal ________ and triangular ________ that meet at a common point called the ________. The ________ of a pyramid is the total area of all its faces. The height of each triangular face is known as the ________ height.
Explain how the surface area of a square pyramid changes if you double the side length of the base and the slant height. Justify your answer with mathematical reasoning.
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