The document discusses three-dimensional shapes, highlighting their properties such as faces, edges, and vertices, which distinguish them from two-dimensional shapes. It explains the definitions of convex and concave polyhedra, as well as regular polyhedra, and includes examples like cubes and pyramids. Additionally, it covers the concept of map scaling, emphasizing the importance of accurately representing distances on maps for practical applications.

2. Different type of shapes
•Euler’s formula
3D Shapes
Drawing a map

4. • Three-dimensional shapes have four
properties that set them apart from two-
dimensional shapes: faces, vertices, edges
and volume.
• These properties not only allow to
determine whether the shape is two- or
three-dimensional, but also which three-
dimensional shape it is.

5. • The part of the shape
that is flat or curved.
• E.g. : Cube has six
faces

6. • The part of the shape
where two faces meet.
• E.g. : Cube has twelve
edges

7. • The part of the
shape where
three or four
edges meet
• E.g. : Pyramid
has four edges

8. Platonic
Solid
Picture
Number
of Faces
Shape of
Faces
Number
of Faces
at Each
Vertex
Number
of
Vertices
Number
of Edges
Unfolded
Polyhedron (Net
etrahedron 4
Equilateral
Triangle
(3-sided)
3 4 6
Cube 6
Square
(4-sided)
3 8 12
Octahedron 8
Equilateral
Triangle
(3-sided)
4 6 12
odecahedron 12
Regular
Pentagon
(5-sided)
3 20 30
cosahedron 20
Equilateral
Triangle
(3-sided)
5 12 30

9. Top view
Front view
Side view

10. Object
Top view
Front
view
Side view

11. • A map is a scaled graphic representation of a
portion of the earth's surface.
• The scale of the map permits the user to
convert distance on the map to distance on the
ground or vice versa.
• The ability to determine distance on a map, as
well as on the earth's surface, is an important
factor in planning and executing military
missions.

12. • Distances Shown on the map are proportional
to the actual distance on the ground.
• While drawing a map, we should take care
about:
How much of actual distance is denoted by :
1mm or 1cm in the map
• It can be : 1cm = 1 Kilometres or 10 Km or
100Km etc.
• This scale can vary from map to map but not
within the map.

16. A polyhedron is said to be convex if
its surface (comprising its faces,
edges and vertices) does not
intersect itself and the line segment
joining any two points of the
polyhedron is contained in the
interior or surface.

17. A polyhedron is said to be concave if
its surface (comprising its faces,
edges and vertices) intersect itself
and the line segment joining any two
points of the polyhedron is
contained in the interior or surface.

18. A polyhedron is said to be regular if
its faces are made up of regular
polygons and the same number of
faces meet at each vertex