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The Pyramid

The Pyramid. Geometric Solids:. Solid Geometry. Our Second Solid: The Pyramid. Pyramids can be Regular or Irregular. A regular pyramid has a base which is always a regular polygon. If the base is NOT a regular polygon then the entire Pyramid is Irregular.

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The Pyramid

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  1. The Pyramid Geometric Solids:

  2. Solid Geometry

  3. Our Second Solid: The Pyramid Pyramids can be Regular or Irregular. A regular pyramid has a base which is always a regular polygon. If the base is NOT a regular polygon then the entire Pyramid is Irregular. Pyramid- A three-dimensional figure made up of a base and triangular faces that meet at the vertex, V, which is also called the apex of the pyramid.

  4. The Number of Faces • The number of triangular faces depends on the number of sides of the base.  For example, a pyramid with a rectangular base has four triangular faces, a pyramid with a hexagonal face is made up of six triangular faces so on…

  5. Parts of the Pyramid apex altitude . The lateral faces all intersect at a point called the apex and form triangles. The altitude is a segment from the vertex perpendicular to the base. The slant height is the height of a lateral face. Lateral side Slant height Base

  6. Regular Pyramids Formulas Lateral Area: L.A. = ½ lp (p = perimeter, l = slant height) Surface Area: S.A. = ½ lp + B (B = area of base) Volume: V = ⅓ Bh ( B = area of base, h = height)

  7. Example 1 of a Regular Pyramid 13 12 10 10 Perimeter of Base = (2 x 10) + (2 x 10) = 40 Slant height l = 13 ; Height h = 12 Lateral area = ½ lp = ½ (13)(40) = 260 sq. units Area of base = 10 x 10 = 100 sq. units Surface area = 260 + 100 = 360 sq. units Volume = ⅓ (100)(12) = 400 cubic units

  8. Example 3: Complete the table for the regular square pyramid.

  9. Example 3: Answers

  10. Example 4: Find the height of a square pyramid with a base area of 16 cm2 and a volume of 32 cm3. The height is 6 cm.

  11. Examples 5-7 LA = 260 TA = 360 LA = 96 TA = 96+16√3 LA = 180 TA = 180+108√3

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