LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

VOLUME AREA PERIMETER

__INTRODUCTION__

**Basically measurement
of the perimeter, volume, and area are required to calculate at the time of making
any diagram, construction, or repairing of any solid construction, wooden,
plastic, or any other article or material. There are some easy methods to
calculate via applying formula depend on the diagram.**

__PERIMETER –____
__**Perimeter is the boundary of a figure**

**RECTANGLE-**** **

**As we all know that, the above picture or diagram is of Rectangle and in Rectangle there are two
opposite sides that are equal in the length and the width. Here ‘L’ defines length and ‘W’
defines width of this rectangle, therefore perimeter of a Rectangle is **

** = L + W + L + W
= L + L + W + W = 2 L + 2 W **

** =
2 ( L + W ) = 2 ( Length + Width)**

**The opposite side of
Length and Width of Rectangle must be the same units while calculating the
Perimeter of Rectangle**

__SQUARE____ __

**As we all know that, the above picture or diagram is of a Square and in a Square there are all sides should
be equal in length. Here ‘a’ defines the length of each side of this rectangle,
therefore perimeter of a Rectangle is **

**= a + a + a + a = 4 a **

**= 4 x Length of One side **

**Each opposite side of the Length and the Width of Rectangle must be the same units while calculating the
Perimeter of Rectangle.**

__TRIANGLE__

**As we all know that, the above picture or diagram is of a Triangle and in Triangle, all sides may be equal
or may not be equal in length. Here ‘b’ defines each side of this Triangle,
therefore perimeter of a Triangle is. **

**Perimeter of a
Triangle = Sum of its 3 sides **

** = b + b + b **

**The Perimeter of a
Triangle is the sum of the measure of the 3 sides.**

__AREA –__** The a****rea of a given figure is defined as the
amount of surface covered by a figure. The area is always measured in square unit.**

**RECTANGLE -**

**The above picture or
diagram is of Rectangle and in Rectangle there are two opposite sides that are equal
in length and width. Here ‘A’ defines the length and ‘B’ defines the width of this
rectangle.**

**The area of a Rectangle
is to be described by multiplication of Length and Width of a Rectangle and the unit
should be measured by the square unit.**

**Area of a Rectangle
= A x B = AB**

__Unit used for the measurement of
Area -__

**1) Small
surface area is measured as square millimeter (mm²), square centimeter (cm²),
square decimeter (dm²).**

**2) Large
surface area is measured as square meter (m²), square decameter (dam²), square
hectometer (hm²).**

**3) More than
large surface are described as square kilometer (km²) **

**Above the picture you can
observe that, there is a rectangle with 4 cm length and 3 cm width, and this
rectangle has been divided into 12 no.s blocks of the square. Suppose the area of
each square is 1 cm² (sq cm) **

**Area of rectangle =
Length x Width **

** = 4 x 3 = 12 sq cm (cm²) [ as per formula ] **

**
= number of unit squares
in the rectangle**

__We
can observe from the above rectangle figure-__

**The number of square
along the length is 4 no.s and the number of square along the width is 3 no.s**

**If we multiply the
square block number obtained from rectangle length & width wise , then 3 x
4 = 12 no.s square blocks. So, the area of each square block is = 12 sq cm (cm²) /
12 blocks **

** = 1 sq cm (cm²) / 1 block .**

**So, the area of each
square block is 1 sq cm (cm²).**

__SQUARE__

**As we all know that, a square is a type of rectangle where all sides are equal. **

**So, the area of a square
is **

**= one side (length) x another side (width) **

**= a x a = a²**

__TRIANGLE __

**From the above shape, you
can observe that there is a triangle with height ‘H’ and base ‘B’.**

** XY = Height =
‘H’, **

** YZ = Base = ‘B’, **

** XZ = Diagonal = ‘D’**

** So, the area of a triangle is**

** = 1/2 x Base x Height **

**= 1/2 x B x H**

**On the other way, we
can use the area of a rectangle to find the area of the triangle**

**From the above picture we
can observe the diagram of a Rectangle KLMN, between rectangle draw diagonal KM, Now we have two congruent right angle KLM & MNK**

**For Rectangle , KN
= LM = b and KL = NM = a**

**So, the area of the rectangle = Length x Width **

** = KL x KN or LM x NM or NM x KN or KL x
LM**

**
=
a x b **

**Now, the area of
Triangle = 1/2 x area of Rectangle **

**
= 1 / 2 x a x b = 1/2 ab **

**And the Diagonal of
any ‘Rectangle’ is = √ (Length)² + (Width)² **

**
= √ a² + b²**

__VOLUME –__

**The amount of space
taken by a solid is known as it’s volume**

**As we all know, the above
picture or diagram is of the cube.**

**In every cube, there
are Length, Height and Width**

**As we know that,
every side of Cube is equal to each other. So, If Height is ‘A’, then Width is
‘A’ and Length is ‘A’, then the volume of cube must be –**

**
Volume of Cube = Length x Width x Height**

** = A
x A x A**

**
= A³**

__Unit
used for the measurement of Volume-__

**1) Small
covered area is measured as cubic millimeter (mm³), cubic centimeter (cm³),
cubic decimeter (dm³).**

**2) Large
covered area is measured as cubic meter (m³), cubic decameter (dam³), cubic
hectometer (hm³).**

**3) More than
large covered are described as cubic kilometer (km³).**