1 / 7

Section 9.2 Pyramids, Area, & Volume

Learn about pyramids, their properties, and how to calculate their lateral surface area, total surface area, and volume. Explore the Pythagorean Theorem as it applies to pyramids.

murillob
Download Presentation

Section 9.2 Pyramids, Area, & Volume

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Section 9.2Pyramids, Area, & Volume Section 9.2 Nack/Jones

  2. Pyramid • The solid figure formed by connecting a polygon with a point not in the plane of the polygon is called a pyramid. • The polygonal region is called the base & the point is the vertex. • A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent. • The slant height of a regular pyramid is the altitude from the vertex of the pyramid to the base of any of the congruent lateral faces of the regular pyramid. • The line segment from the vertex perpendicular to the plane of the base is the altitude. Ex. 1 p. 415 Section 9.2 Nack/Jones

  3. Pyramid • In the regular pyramid, the distance l is called the slant height of the lateral surfaces of a regular pyramid. • Theorem 9.2.1: In a regular pyramid, the length a of the apothem of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem, that is l² = a² + h² in every regular pyramid. l h a Section 9.2 Nack/Jones

  4. LateralSurface Area of a Pyramid • Theorem 9.2.2: The Lateral Area L of a regular pyramid with slant height l and perimeter P of the base is given by: L = ½ pl It is simpler to find the area of one lateral face and multiply by the number of faces. Example 2 p. 415 Section 9.2 Nack/Jones

  5. Total Surface Area • Theorem 9.2.3: The total area (surface area) T of a pyramid with lateral area L and base area B is given by ( the sum of the area of all its faces): T = L + B or T = ½ pl + B Example: To find the total area, Find the slant height. Apply Pythagorean Theorem to one face: l ² + 2² = 6² or l = 42 Find Lateral Area: L = ½ pl= ½42 (16) = 32 2 Find the area of the Base: 6 B = 16 l Total Area = 16 + 32 22 6 4 Section 9.2 Nack/Jones

  6. Volume of a pyramid • Theorem 9.2.4: The volume V of a pyramid having a base area B and an altitude of length h is given by: V =1/3 Bh Example 6 p. 419:h = 12, side = 4 Find the area of the base: B = ½aP. Since it is a 30-60-90 triangle, we know that a = 23 B = ½ 23 (64) = 24 3 V =1/3 Bh = 96 3 units3 Section 9.2 Nack/Jones

  7. Another application of the Pythagorean Theorem • Theorem 9.2.5: In a regular pyramid, the lengths of altitude h, radius r of the base and lateral edge e satisfy the Pythagorean Theorem, that is: e² = h² + r² Example 5 p. 418 Section 9.2 Nack/Jones

More Related