Shapes can be described mathematically and classified based on their dimensions. Two-dimensional shapes like circles are flat, while three-dimensional shapes like cubes have length, width, and height. Polyhedrons are solid shapes with polygon faces, vertices where edges meet, and edges where faces meet. Polyhedrons follow Euler's formula relating faces, vertices and edges. Regular polyhedrons have identical regular polygon faces meeting at each vertex. Prisms have two parallel congruent polygon bases connected by parallelogram sides, and pyramids have a polygon base and triangular faces meeting at a common vertex above the base.

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 two-
dimensional 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. They depend
on only two coordinates--x and y, for instance--
consisting of x units and y units, respectively. 2-D
shapes include the square, the triangle, the
rhombus, etc.
2-D shapes do not have prominent or rugged
parts. For example, square, whereas three-
dimensional like 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
3-dimensional shapes have four properties that
set them apart from two-dimensional shapes:
• faces,
• vertices,
• edges and
• volume.
These properties determine whether the shape
is two- or 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. 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.
Colors used in Map

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.
Scales used in Maps

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

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
of Faces
Shape of
Faces
Number
of Faces
at Each
Vertex
Number
of
Vertices
Number
of Edges
Unfolded
Polyhedron (Net)
Tetrahedron 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
Dodecahedron 12
Regular
Pentagon
(5-sided)
3 20 30
Icosahedron 20
Equilateral
Triangle
(3-sided)
5 12 30

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. A polyhedron is a solid shape bounded by polygons whereas non-
polyhedrons 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.
Polyhedrons
These are polyhedrons. These are not polyhedrons.
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. 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.
Polyhedrons
Irregular polyhedron
Regular polyhedron

20. 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.
Polyhedrons
Convex polyhedron

21. 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 and pyramids
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