the pyramid
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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The PyramidThe PyramidGeometric Solids:
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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.
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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.
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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…
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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
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Regular Pyramids FormulasRegular Pyramids Formulas
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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
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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
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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
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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.
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Examples 5-7 Examples 5-7
LA = 260TA = 360
LA = 96TA = 96+16√3
LA = 180TA = 180+108√3