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1. 发展经济学1
MENSURATION
PRESENTED BY
1. ARJUN RASTOGI

2. What is Mensuration
 Mensuration in its literal meaning is
to measure, Its generally used where
geometrical figures are concerned,
Where one has to determine various
physical quantities such as area ,
volume , length measuring these
quantities is called mensuration also
it is used where quantities like
speed, velocity and acceleration etc
are concerned

3. 2D SHAPES
• A shape that only has two dimensions
(such as width and height) and no
thickness. Squares, Circles, Triangles, etc
are two dimensional objects.
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4. SOME OF SHAPES IN MENSURATION
2D
1) Square
 2) Rectangle
 3) Parallelogram
 4) Rhombus
5) Triangle
6) Trapezoid
7) Circle

5. a square is a regular quadrilateral, which
means that it has four equal sides and four
equal angles (90-degree angles, or right
angles). It can also be defined as
a rectangle in which two adjacent sides
have equal length. A square
with vertices ABCD would be
denoted ABCD.

6. PERIMETER
• The Perimeter is
• 4 times the side length
Perimeter = 4a
• Perimeter is the distance
around a closed figure and is
typically measured in
millimeters (mm), centimeters
(cm), meters (m) and
kilometers (km). These units
are related as follows:
• 10 mm = 1 cm
• 100 cm = 1 m
• 1000 m = 1 km
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7. AREA
 AREA OF SQUARE IS

8.  A rectangle is any quadrilateral with four right
angles. It can also be defined as an equiangular
quadrilateral, since equiangular means that all of
its angles are equal (360°/4 = 90°).. A rectangle
with four sides of equal length is a square. The
term oblong is occasionally used to refer to a
non-square rectangle A rectangle
with vertices ABCD would be denoted
as ABCD.

9. PERIMETER
The Perimeter is
2 times the (width +height )
Perimeter = 2(w+h)
W = width
H = height

10. AREA
The Area is
the width times
the height
Area = w × h
Width =w
Height = h

11. A parallelogram is a (non self-intersecting)
quadrilateral with two pairs
of parallel sides. The opposite or facing
sides of a parallelogram are of equal
length and the opposite angles of a
parallelogram are of equal measure

12. 12
PERIMETER
• The Perimeter is
2 times the (base +
side length):
• Perimeter = 2(b+s)

13. AREA OF PARALLELOGRAM
• The Area is the
• base times the height:
• Area = b × h
• (h is at right angles to b)
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14. a rhombus , is a simple (non-self-intersecting)
quadrilateral all of whose four
sides have the same length. Another name
is equilateral quadrilateral, since
equilateral means that all of its sides are
equal in length. The rhombus is often
called a diamond

15. PERIMETER
The Perimeter is
4 times "s" (the side
length)
because all sides are
equal in length:
Perimeter = 4s

16. AREA OF RHOMBUS
Area of rhombus
the altitude times the side
divided by 2
Area = (p × q)/2
Rhombus = side length
of rhombus
h = height of rhombus
d1 = long diagonal of rhombus
d2 = short diagonal of
rhombus

17.  A triangle is a polygon with
three edges and three vertices. It is one
of the basic shapes in geometry. A
triangle with vertices A, B, and C is
denoted
 TYPES OF TRIANGLE
1. ISOSCLES
2. EQUILATERAL
3. SCALENE

18. •
PERIMETER
•Perimeter of triangle
Sum of sides
3s
As perimeter is sum of
sides which can be also
written as
P=A+B+C

19. AREA OF TRIANGLE
A triangle is half the area of a
rectangle. To find the area of a
triangle, you use the rectangle
formula (base times height)
and divide it in half.
A = base • height
2

20. A convex quadrilateral with at least one
pair of parallel sides is referred to as
a trapezoid . The parallel sides are called
the bases of the trapezoid and the other
two sides are called the legs or the lateral
sides (if they are not parallel; otherwise
there are two pairs of bases).

21. Perimeter of trapezoid
the sum of all side lengths:
Perimeter = a+b+c+d

22. Area of trapezoid
• The area of a polygon is the number of square
units inside that polygon. Area is 2-dimensional
like a carpet or an area rug. A trapezoid is a 4-
sided figure with one pair of parallel sides. For
example, in the diagram to the right, the bases
are parallel. To find the area of a trapezoid, take
the sum of its bases, multiply the sum by the
height of the trapezoid, and then divide the
result by 2, The formula for the area of a
trapezoid is
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23. A circle is a simple shape Of that is the
set of all points in a plane that are at a
given distance from a given point,
the centre. The distance between any of
the points and the centre is called
the radius. It can also be defined as the
locus of a point equidistant from a fixed
point.

24. The perimeter is of circle
2 times radius into pi
Circumference = 2 × π × r

25. AREA OF CIRCLE
The Area is the
side length squared:
Area = a2 = a × a
The distance around a circle is called
its circumference. The distance across a
circle through its center is called
its diameter. We use the Greek letter
The area of a circle is the number of square
units inside that circle

27. INTRODUCTION
 TOTAL SURFACE AREA(TSA)
Total surface are is the sum of the areas of all the sides
of Three dimensional figure
 LATERAL SURFACE AREA (LSA)
Lateral area refers to the surface area of a 3D object
such as prism, cylinder, cone etc., Lateral surface
area is the sum of all sides of a 3D object except its
top and bottom bases.
 VOLUME
The amount of 3-dimensional space an object
occupies. Capacity.

28. 3D SHAPES
An object that has height, width and depth,
like any object in the real world.

29. SOME OF SHAPES IN
MENSURATION
3D
 1) Cube
2) Rectangular
Prism (Cuboids)
 3) Cylinder
4) Cone
5) Sphere and
Hemisphere
6) Prism
7) Pyramid

30. A cuboid is a box-shaped solid object. It
has six flat sides and all angles are right
angles.
And all of its faces are rectangles.

31.  Lateral surface area of the
cuboid
= perimeter of rectangular
base * height
= 2(l + w)h square units
= 2h(l + w) square units
Total surface area of the
cuboid
= lateral surface area + area of
base + area of top
= [2h(l + w) + lw + lw] square
units
= (2hl + 2hw + 2lw) square
units
= [2(lh + wh + lw)] square units

32.  a cube is a three-dimensional solid object
bounded by six square faces, facets or
sides, with three meeting at each vertex.

33. THE TSA OF CUBE
IS =6A2
The LSA OF CUBE
IS
=4A2
VOLUME OF CUBE
 =A 3

34.  A cone is a three-dimensional geometric
shape that tapers smoothly from a flat
base (frequently, though not necessarily,
circular) to a point called the apex or
vertex.

35. Total surface area = rlπ + πr²
 lateral surface area of a cone = πrl
Volume of a cone

36.  cylinder is one of the most basic
curvilinear geometric shapes, the surface
formed by the points at a fixed distance
from a given line segment, the axis of the
cylinder.

37. The total surface area (TSA) of
a cylinder with radius r and
height h is
 LSA OF CYLINDER=2πrh
Volume OF CYLINDER=
πr2h

38. PYRAMID
A pyramid is a structure whose outer
surfaces are triangular and converge to a
single point at the top, making the shape
roughly a pyramid in the geometric sense.

39. TOTAL SURFACE AREA =
LATERAL SURFACE
AREA=
VOLUME=Area of the
base * Height * 1/3

40. a solid geometric figure whose two ends
are similar, equal, and parallel rectilinear
figures, and whose sides are
parallelograms.

41. PRISM
TOTAL SURFACE =LSA +
2B (lateral surface area x
area of the base)
Lateral surface area =p x
h (perimeter of the base x
the height)
VOLUME=B x h (area of
the base x height)

42. A sphere is a perfectly round geometrical
and circular object in three-dimensional
space that resembles the shape of a
completely round ball.

43. SPHERE
TOTAL SURFACE AREA=4πr2
VOLUME=4/3πr3