Download PreAP Geometry 6.2 Notes RHS-Niven 3-Dimensional

PreAP Geometry
6.2 Notes
RHS-Niven
3-Dimensional figure = Solid figure = polyhedron
Prism – a 3-dimensional solid with two congruent, polygonal and parallel bases, whose other faces are
called lateral faces.
Faces - the polygons that make up a 3-dimensional figure. Know difference between base and lateral face.
Edge – is the intersection of any two faces. Know difference between base edge and lateral edge.
Vertex – a point at the intersection of 3 or more faces.
Naming Prisms – Prisms are named according to their base shape and whether they are right or oblique.
______________
1st word
Base shape (Adj.)
_____________ Prism
2nd word
3rd word
right or oblique Prism
ex. Hexagonal Oblique Prism
ex. Rectangular Right Prism
In an oblique prism, the edges of the faces connecting the bases are not perpendicular to the bases. In a
right prism, those edges are perpendicular to the bases.
If the segment connecting the two centers of the bases is perpendicular to each of the bases, then the
prism is said to be a Right Prism.
There are 2 different types of surface areas:
1. Lateral surface area
2. Total surface area
Lateral Surface Area – SL – Is the sum of the areas of the lateral faces.
Total Surface Area – ST – Is the sum of ALL the areas of the faces. It is the lateral surface area plus the area
of the base(s).
SL of prisms =
where is the perimeter of a Base and is the height of the prism. The height of the
prism is the perpendicular distance between the two Bases.
ST of prisms =
where
is the area of a Base.
Ex1. Lateral surface area of a square right prism
SL =
SL =
Ex5. Lateral surface area of a rectangular right prism
SL =
SL =
Ex2. Total surface area of a square right prism
ST =
ST =
Ex6. Total surface area of a rectangular right prism
ST =
ST =
Ex3. Later surface area of a triangular right prism
SL =
SL =
Ex7. Later surface area of a regular pentagonal right prism
SL =
SL =
Ex4. Total surface area of a triangular right prism
ST =
ST =
Ex8. Total surface area of a regular pentagonal right prism
ST =
ST =
PreAP Geometry
6.2 Notes
RHS-Niven
Cylinder – “Prism” with circular Bases. It is a solid with two congruent circular bases that lie in parallel
planes.
The height of a cylinder is the perpendicular distance between its Bases.
The radius of a Base is the radius of the cylinder
In a right cylinder, the segment joining the centers of the bases is perpendicular to the bases. Whereas in
an oblique cylinder the segment joining the centers of the bases is NOT perpendicular.
SL of cylinder =
where is the radius of the cylinder and is the height of the cylinder.
This is the same as SL =
where stands for circumference of a Base.
ST of cylinder =
This is the same as SL =
for the area of the Base.
where
.
stands for circumference of a Base.
and
stands
Pyramid – is a polyhedron in which the base is a polygon and the lateral faces are triangles with a common
vertex, called the vertex of the pyramid.
The intersection of two lateral faces is a lateral edge and the intersection of the base and a lateral face is a
base edge.
The height of the pyramid is the perpendicular distance between the base and the common vertex.
If the segment connecting the common vertex and center of the base is perpendicular to the base, then the
pyramid is said to be a Right Pyramid.
In an oblique pyramid, the intersection of the lateral faces (the common vertex) is not directly over the
center of the base as it is in a right pyramid.
Naming Pyramids – pyramids are named according to their base shape and whether they are right or
oblique. Very similar to prisms.
SL of pyramids =
where is the perimeter of the Base and is the slant height of the pyramid. The
slant height of a pyramid is the length of the segment from the common vertex and is perpendicular to a
base edge.
ST of pyramids =
where
is the area of the Base.
Ex1. Lateral surface area of a square right pyramid
SL =
SL =
Ex5. Lateral surface area of a rectangular right pyramid
SL =
SL =
Ex2. Total surface area of a square right pyramid
ST =
ST =
Ex6. Total surface area of a rectangular right pyramid
ST =
ST =
Ex3. Later surface area of a triangular right pyramid
SL =
SL =
Ex7. Later surface area of a regular pentagonal right pyramid
SL =
SL =
Ex4. Total surface area of a triangular right pyramid
ST =
ST =
Ex8. Total surface area of a regular pentagonal right pyramid
ST =
ST =
PreAP Geometry
6.2 Notes
RHS-Niven
Cone – is the union of all segments in space that join points on a circle to a point (called the vertex of the
cone) that is not coplanar with the circle. The base of a cone is the intersection of a cone and a plane.
If the segment that joins the center of the circular base to the vertex is perpendicular to the plane that
contains the center, the cone is a right cone and the segment is called the height of the cone. Otherwise,
the cone is oblique.
The height of a cone is the perpendicular distance between the vertex and the base.
The radius of the Base is the radius of the cone
SL of cone =
ST of cone =
where is the radius of the cylinder and is the slant height of the cone.
later area plus the area of the one circular base