Shapes and Forms

Geometric shapes ; regular and irregular plane types and solids and their characteristics

1. Characteristics of planes
& solids
Ar. Surashmie Kaalmegh
Asisstant Professor
LAD College , Nagpur

2. In the subject we learn …
Orthographic
projections
Interpenetration
Development of solids.

Scales
 Isometric projections
Perspective view

3. Drawing elements
Point
Line
Plane
Colour
Texture

4. Points

5. Lines:

7. Planes :

8. Colours

9. Texture

11. Some basics :

12. Lines & Planes :

13. Regular Solids

15. Characteristics
Faces /
Surfaces
Edges
Vertices

16. Each face is a plane ……

18. Construction of a Solid

19. Solids have volumes…

20. The pyramid :

22. A pyramid is a three-dimensional figure with a single base and a three or
more non-parallel sides that meet at a single point above the base. The
sides of a pyramid are triangles.

A regular pyramid is a pyramid that has a regular polygon for its base and
whose sides are all congruent triangles.

23. Properties of a Regular Pyramid
 The edges of a regular pyramid are
equal; it is denoted by e.
The lateral faces of a regular pyramid
are congruent isosceles triangles .
The altitudes of the lateral faces of a
regular pyramid are equal. It is the
slant height of the regular pyramid and
is denoted by L.
The altitude of the regular pyramid is
perpendicular to the base. It is equal
to length of the axis and is denoted by
h.
The vertex of regular pyramid is
directly above the center of its base
when the pyramid is oriented as shown
in the figure.
If a cutting plane is passed parallel
to the base of regular pyramid, the
pyramid cut off is a regular pyramid
similar to the original pyramid.

24. Cone :

25. The slant height of a right circular
cone is the length of an element.
Both the slant height and the
element are denoted by L.
The altitude of a right circular is
the perpendicular drop from
vertex to the center of the base. It
coincides with the axis of the right
circular cone and it is denoted by h.
If a right triangle is being revolved
about one of its legs (taking one
leg as the axis of revolution), the
solid thus formed is a right
circular cone.
 The surface generated by the
hypotenuse of the triangle is the
lateral area of the right circular cone
and the area of the base of the cone
is the surface generated by the leg
which is not the axis of rotation.
All elements of a right circular cone
are equal.
Any section parallel to the base is
a circle whose center is on the
axis of the cone.
A section of a right circular cone
which contains the vertex and two
points of the base is an isosceles
triangle.

26. Properties of a Cone
An element of a cone is the
generator in any particular
position.
The altitude of the cone is
the perpendicular drop from
vertex to the plane of the
base. It is denoted as h.
Every section of a cone
made by a plane passing
through its vertex and
containing two points of the
base is a triangle. See section
PQV, where V is the vertex and P
and Q are two points on the base.
The axis of the cone is the
straight line joining the
vertex with the centroid of
the base.
For right cone, altitude and
axis are equal in length.
The right section of a cone
is a section perpendicular
to its axis and cutting all
the elements. For right
cone, the right section is
parallel and similar to the
base. Right section is
denoted by AR.
A circular cone is cone
whose right section is a
circle.

29. Complex solids :