Mensuration

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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. 发展经济学 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.

4. SOME OF SHAPES IN MENSURATION
2D
1) Square
2) Rectangle
3) Parallelogram
4) Rhombus
5) Triangle
6) Trapezoid
7) Circle

5. asquareis aregularquadrilateral, which
means that it has four equal sides and four
equalangles(90-degreeangles, orright
angles).It can also be defined as
arectanglein which two adjacent sides
have equal length. A square
withverticesABCD would be
denotedABCD.

6. 发展经济学 6
PERIMETER
•The Perimeter is
•4 times the side length
Perimeter = 4a
•Perimeteris 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

7. AREA
AREA OF SQUARE IS

8. A rectangleis anyquadrilateralwith fourright
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 asquare. The
termoblongis occasionally used to refer to a
non-squarerectangle A rectangle
withverticesABCDwould be denoted
asABCD.

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

10. AREA
The Area is
thewidthtimes
theheight
Area = w ×h
Width =w
Height = h

11. Aparallelogramis a (non self-
intersecting)quadrilateralwith two pairs
ofparallelsides. 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. 发展经济学 13
AREA OF PARALLELOGRAM
•The Area is the
•base times the height:
•Area = b ×h
•(his at right angles tob)

14. arhombus, is asimple(non-self-
intersecting)quadrilateralall of whose four
sides have the same length. Another name
isequilateral quadrilateral, since
equilateral means that all of its sides are
equal in length. The rhombus is often
called adiamond

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

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

17. Atriangleis apolygonwith
threeedgesand threevertices. It is one
of the basicshapesingeometry. A
triangle with verticesA,B, andCis
denoted
TYPES OF TRIANGLE
1.ISOSCLES
2.EQUILATERAL
3.SCALENE

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

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.
2
A = base •height

20. Aconvexquadrilateralwith at least one
pair ofparallelsides is referred to as
atrapezoid. The parallel sides are called
thebasesof the trapezoid and the other
two sides are called thelegsor 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. 发展经济学 22
Area of trapezoid
•The area of apolygonis 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 ofparallelsides. 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

23. Acircleis a simpleshapeOf that is the
set of allpointsin aplanethat are at a
given distance from a given point,
thecentre. The distance between any of
the points and the centre is called
theradius. 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 acircleis called
itscircumference. The distance across a
circle through its center is called
itsdiameter. 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. acubeis athree-dimensionalsolid object
bounded by sixsquarefaces,facetsor
sides, with three meeting at each vertex.

33. THE TSA OF CUBE
IS =6A2
The LSA OF CUBE
IS
=4A2
VOLUME OF CUBE
=A3

34. Aconeis 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. cylinderis 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. Thetotal surface area (TSA)of
acylinderwith radiusrand
heighthis
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=4πr 2
VOLUME=4/3πr 3