发展经济学 1

MENSURATION

PRESENTED BY

1. ARJUN RASTOGI

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

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.

SOME OF SHAPES IN MENSURATION

2D

1) Square

2) Rectangle

3) Parallelogram

4) Rhombus

5) Triangle

6) Trapezoid

7) Circle

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.

发展经济学 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

AREA

AREA OF SQUARE IS

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.

The Perimeter is

2 times the (width +height )

Perimeter = 2(w+h)

W = width

H = height

PERIMETER

AREA

The Area is

the width times

the height

Area = w × h

Width =w

Height = h

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

PERIMETER

• The Perimeter is

2 times the (base +

side length):

• Perimeter = 2(b+s)

发展经济学 13

AREA OF PARALLELOGRAM

• The Area is the

• base times the height:

• Area = b × h

• (h is at right angles to b)

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

The Perimeter is

4 times "s" (the side

length)

because all sides are

equal in length:

Perimeter = 4s

PERIMETER

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

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

•

•Perimeter of triangle

Sum of sides

3s

As perimeter is sum of

sides which can be also

written as

P=A+B+C

PERIMETER

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

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).

Perimeter of trapezoid

the sum of all side lengths:

Perimeter = a+b+c+d

发展经济学 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

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.

The perimeter is of circle

2 times radius into pi

Circumference = 2 × π × r

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

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.

3D SHAPES

An object that has height, width and depth,

like any object in the real world.

SOME OF SHAPES IN

MENSURATION

3D

1) Cube

2) Rectangular

Prism (Cuboids)

3) Cylinder

4) Cone

5) Sphere and

Hemisphere

6) Prism

7) Pyramid

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.

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

a cube is a three-dimensional solid object

bounded by six square faces, facets or

sides, with three meeting at each vertex.

THE TSA OF CUBE

IS =6A2

The LSA OF CUBE

IS

=4A2

VOLUME OF CUBE

=A 3

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.

Total surface area = rlπ + πr²

lateral surface area of a cone = πrl

Volume of a cone

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.

The total surface area (TSA) of

a cylinder with radius r and

height h is

LSA OF CYLINDER=2πrh

Volume OF CYLINDER=

πr2h

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.

TOTAL SURFACE AREA =

LATERAL SURFACE AREA=

VOLUME=Area of the base * Height * 1/3

a solid geometric figure whose two ends

are similar, equal, and parallel rectilinear

figures, and whose sides are

parallelograms.

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)

A sphere is a perfectly round geometrical

and circular object in three-dimensional

space that resembles the shape of a

completely round ball.

SPHERE

TOTAL SURFACE AREA=4πr2

VOLUME=4/3πr3