2. Surface area & Volume of Pyramids Tutorial 13d

3. Pyramids §A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid). Lateral edge The vertex Lateral face base

4. Pyramids §You can name a pyramid by the shape of its base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height h of the pyramid. The vertex Altitude base

5. Pyramids §A regular pyramid is a pyramid whose base is a regular polygon. The lateral faces are congruent isosceles triangles. The slant height l is the length of the altitude of a lateral face of the pyramid. Slant height height

6. §The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height. §The surface area of a regular pyramid is the sum of the lateral area of the base. B l Area Theorem

7. Example #1 l l 5 ft 9 a 2 + b 2 = c 2 9 2 + 5 2 = l 2 81 + 25 = l 2 106 = l 2 10.3  l Use Pythagorean Theorem to find the slant height. Find the Surface Area of this square pyramid.

8. Volume of a Pyramid §The volume of a pyramid is one third the product of the area of the base and the height of the pyramid. h B

9. Example §Find the volume of this regular square pyramid 40 25 ft 20 ft h h 20 2 + h 2 = 25 2 400 + h 2 = 625 h 2 = 225 h = 15 Use Pythagorean Theorem to find the height.