3. What Are Shapes?
A shape is a geometrical figure that
can be described with mathematics. One
way to classify shapes is to describe a
bigger shape that the shape fits inside of.
For example, two-dimensional shapes
like circles will fit inside of a flat plane.
Three-dimensional objects like cubes will
not fit inside of a plane, because they
are not flat.

4. 2-dimensional
Shapes
These
are
twodimensional shapes or
flat
plane geometry
shapes. Their sides are
made of straight or
curved lines. They can
have
any
number
of sides. Plane figures
made
of
lines
are
called polygons.
Triangles and squares
are
examples
of
polygons

5. Properties Of 2
Dimensional Shapes
Two-dimensional shapes are planar. Graphically speaking,
they depend on only two coordinates--x and y, for instance-consisting of x units and y units, respectively. In the case of
a coordinate system of more than two dimensions, then a 2-D
shape would still depend on two coordinate directions. For
example, in a spatial xyz coordinate system (which is threedimensional) a two-dimensional shape would be expressed
with points such as (x,y,0), (x,0,z), or (0,y,z). Therefore, it
would depend on either x and y, x and z, or y and z.
2-D shapes include the square, the triangle, the rhombus, etc.
To understand it more easily, you can say that 2-D shapes do
not have prominent or rugged parts. For example, speaking
two-dimensionally you would have a square, whereas threedimensionally you would have a cube, which is like an
extended or prominent square.

6. 3-Dimensional Shapes
A 3D shape is a solid which
encloses a volume and has
length, breadth and height

7. Other 3D shapes

8. Properties Of 3
Dimensional Shapes
Three-dimensional shapes have four
properties that set them apart from
two-dimensional
shapes:
faces,
vertices, edges and volume. These
properties not only allow you to
determine whether the shape is twoor three-dimensional, but also which
three-dimensional shape it is.

9. What is a Map?
A map is a graphic
representation
of
a
portion of the earth's
surface drawn to scale,
as seen from above.
It uses colors, symbols,
scales and labels to
represent
features
found on the ground.

10. Colors used in Map
a. Black. Indicates cultural (man-made) features such as buildings
and roads, surveyed spot elevations, and all labels.
b. Red-Brown. The colors red and brown are combined to identify
cultural features, all relief features, non-surveyed spot elevations,
and elevation, such as contour lines on red-light readable maps.
c. Blue. Identifies hydrography or water features such as lakes,
swamps, rivers, and drainage.
d. Green. Identifies vegetation with military significance, such as
woods, orchards, and vineyards.
e. Brown. Identifies all relief features and elevation, such as
contours on older edition maps, and cultivated land on red-light
readable maps.
f. Red. Classifies cultural features, such as populated areas, main
roads, fire station,and boundaries, on older maps.
g. Other. Occasionally other colors may be used to show special
information. These are indicated in the marginal information as a
rule.

11. Scales used in Maps
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. Scales used in Maps
-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 Kilometers or 10 Km
or 100Km etc.
- This scale can vary from map to map
but not with in the map.

13. Points to remember

A map depicts the location of a particular
object/place in relation to other objects/places.
 Symbols and colors are used to depict the
different objects/places.
 There is no reference or perspective in map,
i.e., objects that are closer to the observer are
shown to be of the same size as those that are
farther away.
 Maps use a scale which is fixed for a
particular map. It reduces the real distances
proportionately to distances on paper.

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

15. Face
• Part of a shape
that is flat.(Or
curved)
• E.g. A cube has 6
of these.

16. Edge
• The line where
two faces meet.
• E.g. A cube has
12 of these.

17. Vertex (Vertices)
• The place where
three or more
edges meet.
• This pyramid
has 4 of these.

18. Polyhedrons
A polyhedron is a solid shape bounded by polygons whereas nonpolyhedrons do not have polygon shaped faces. Cubes, cuboids,
prisms, and pyramids are few examples of polyhedrons. Spheres,
cones and cylinders are a few examples of non-polyhedrons.
These are polyhedrons .
These are not polyhedrons .
The polygonal regions forming the polyhedron are known as its
faces, two intersecting faces meet at a line segment called an edge
and three edges meet at a point called the vertex.
F+V=E+2 is known as Euler’s formula and it holds true for any
polyhedron. Here F stands for faces, V for vertices and E for the
edges of the polyhedron.

19. Polyhedrons
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. An irregular polyhedron is made of polygons
whose sides and angles are not of equal measure.
Regular polyhedron
Irregular polyhedron

20. Polyhedrons
In a convex polyhedron , the line segment joining any two points
on the surface of the polyhedron lies entirely inside or on the
polyhedron.
A polyhedron some of whose plane sections are concave polygons
is known as a concave polyhedron . Concave polygons have at
least one interior angle greater than 180° and has some of its sides
bent inward.
Convex polyhedron

21. Prisms and pyramids
A prism is a polyhedron with parallel congruent polygon bases and
sides made of parallelograms.
A pyramid is a polyhedron whose base is a polygon of any number
of sides and whose lateral faces are triangles with a common vertex.
Prisms and pyramids are named after the shape of their base.
Maps represent the location of a place or object in relation to other
places or objects.
Prisms
Pyramids

22. Prisms
• Prisms have two identical, parallel
faces joined to one another by
rectangles. Examples are;

23. Pyramids
• Pyramids have one face with at least 3 edges, the faces
meeting these edges are ALL triangles.
NOTE: Pyramids get their name from the shape of their
base.
• There are many more pyramids than these ones shown