The Pyramid Geometric Solids:. Solid Geometry Review: Solid Geometry is the geometry of 3D- dimensional space that we live in. The three dimensions are.

The PyramidThe PyramidGeometric Solids:

Solid GeometrySolid GeometryReview: Solid Geometry is the geometry of 3D-dimensional space that we live in. The three dimensions are width, depth, and height.

Solid Geometry encompasses prisms, pyramids, cones, cylinders, and spheres.

Our Second Solid: The PyramidOur Second Solid: The PyramidPyramid- 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 FacesThe 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 PyramidParts 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 FormulasRegular Pyramids Formulas

Example 1 of a Regular PyramidExample 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 = 260 + 100 = 360 sq. units

Volume = ⅓ (100)(12) = 400 cubic units

10

10

13

12

Example 3: Complete the table Example 3: Complete the table

for the regular square pyramid.for the regular square pyramid.1. 2. 3. 4.

Height 8 12 24 6

Slant Height 10 13 ? ?

Base Edge ? ? 14 ?

Lateral Edge ? ? ? 10

Example 3: AnswersExample 3: Answers1. 2. 3. 4.

Height 8 12 24 6

Slant Height 10 13 25

Base Edge 12 10 14

Lateral Edge10

Example 4: Find the height of a square Example 4: Find the height of a square

pyramid with a base area of 16 cmpyramid with a base area of 16 cm22 and a and a

volume of 32 cmvolume of 32 cm33..

The height is 6 cm.

Examples 5-7 Examples 5-7

LA = 260TA = 360

LA = 96TA = 96+16√3

LA = 180TA = 180+108√3