Plane geometry
Geometry
Solid geometry
flat shapes like lines, curves,
polygons, etc.,
objects of three-dimensional
shapes such as cylinders, cubes,
etc.
Length, width, and height (or depth or thickness) are the three measurements ofspheres,
the threedimensional shapes.
The common elements of a solid shape:
The flat surfaces of the 3D shapes are called the faces.
For polyhedrons:
The line segment where two faces meet is called an edge.
• Straight edges.
A vertex is a point where 3 edges meet
• Flat sides called faces.
Non-flat faces are called curved surface
• Corners, called vertices.
Flat surface (face) which has for of circle calls circular
plane surface
2D–polygon
3D–polyhedron
Polyhedrons (or polyhedra) are straight-sided solid shapes, each face represented by polygon
(triangle, rectangle, rhombus, pentagon….). Polyhedrons are based on polygons, twodimensional plane shapes with straight lines.
Prism: a polyhedron with two congruent and parallel polygonal faces (called bases) and
parallelogram lateral faces.
Base of prism: one of two parallel, congruent sides of an object.
Pyramid: a polyhedron with a polygon for a base and triangles for the lateral faces.
Regular pyramid is a right pyramid with a regular polygon for a base
The names of the prisms and pyramids are based on the bases!!!
How to recognize?
Prisms
• 2 congruent and parallel bases
• Lateral sides are parallelograms
Pyramids
•
Only 1 base
•
Lateral sides are triangles
•
The lateral sides meet together at
an apex
•
The names of the prisms and
pyramids are based on the bases.
2D–parallelogram
Pyramids
• Only 1 base
• Lateral sides are triangles
• The lateral sides meet together at an apex
3D–parallelepiped
Parallelepiped - a polyhedron having six faces (each face is parallelogram) which is termed
as hexahedron. We can say that a parallelepiped is a hexahedron having three pairs of parallel
faces.
Surface area is a sum of all the surfaces (flat or curved) of a solid shape
Lateral surface area is a sum of all the lateral faces (surfaces) of the shape. We can calculate
it as difference of surface area and base (bases) area
Volume is the amount of space that an object occupies.
Slant height of a solid is the distance measured slant from the base to the
vertex along the mid line of the lateral face.
But in the case of a cylinder or a rectangular prism, there is no
distinction between the height and slant height and l = h
Slant - a position that
is leaning or sloping
Drawing 3D shapes in 2D
To draw out the net of the shape means to
draw each and every side (face) flat
To consider what can be seen from different
directions.
Cross section is the intersection of a three-dimensional
object (body) with a plane.
Mainly we consider three types of cross sections:
1) Horizontal
2) Vertical
3) Diagonal
A truncated pyramid is the result of cutting a pyramid by a plane parallel to
the base and separating the part containing the apex.
o The lateral faces of a truncated pyramid
are trapezoids.
o The height of a truncated pyramid is the
perpendicular distance between the bases.
o The apothem is the height of any of its sides.