The Pyramid Geometric Solids:

Solid Geometry Review: Solid Geometry is the geometry of 3D- dimensional space that we live in. The three dimensions are width, depth, and height.geometry Solid Geometry encompasses prisms, pyramids, cones, cylinders, and spheres.

Our Second Solid: The Pyramid 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. 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.

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…

Parts of the Pyramid. 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 apex altitude Slant height Base

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

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

Example 3: Complete the table for the regular square pyramid Height Slant Height1013?? Base Edge??14? Lateral Edge???10

Example 3: Answers Height Slant Height Base Edge Lateral Edge 10

Example 4: Find the height of a square pyramid with a base area of 16 cm 2 and a volume of 32 cm 3. The height is 6 cm.

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