What is Geometry Used For

Introduction:
Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment- Euclidean geometry- set a standard for many centuries to follow. Here in this topic we are going to see what is geometry used for.

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Uses of geometry:


In home or a building geometry is useful in the improvement of projects. For example, to find the area of the floor, height of a building, to place tiles of particular dimension in a particular area, to place furniture in a required place, estimating the fabric needed, to paint the wall how much paint is needed. Geometry is also used to measure volumes. For example, amount of water needed in the fish tank, volume of the paint the wall by the surface area.

Geometry has many uses to find the size, shape, volume, or position of an object. As a school subject, it helps develop logical reasoning. Architects and engineers use geometry in planning buildings, bridges, and roads. Geometry is used by navigators to guide boats, planes, and even space ships. Military personnel use geometry to guide vessels and aim guns and missiles. Almost everything you do in your daily life involves geometry in some way.

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Some problems in geometry:


1) Find the volume paint used to paint the wall. The paint tin in the form of  a cylinder with radius 12 cm and height 19 cm

Given:                     radius r = 12 cm

                                height h = 19 cm  

Solution:

volume of paint = volume of the cylinder

         Volume of a cylinder  =  `pi` r^2 h

                                                =  3.14 (12)^2 19

                                                = 3.14 (144) 19

                                                = 8591.04 cm^3

Therefore the volume of the pait needed to paint the wall is 8591.04 cm^3.

2) A road roller is cylindrical in shape. The radius of the road roller is 35cm. Its length is 120cm. Find the surface area?

Solution

Given: r = 35cm, h = 120cm.

(i) The surface area = 2`pi` r (h +r)

                                = 2`pi` × 35 ( 120 + 35 )

                                = 34,100 cm2.

Geometry Terms Called Plane

Introduction to geometry terms called plane:

A surface which has thickness as zero and infinitely large in geometry terms is called as plane. The plane is imagined in both direction with infinite large length. In geometry, the plane term is two dimension surface and it does not have edges.This is created from analysis of point, line and space in geometry. Please express your views of this topic Define Parallel Lines by commenting on blog.


Explanation for plane in geometry terms


The terms plane is present in geometry:

In Euclidean geometry, the subspace are used for setting the plane and the plane is called in terms of whole space. The trigonometry, geometry terms are use the plane. The plane is consider the group of points and is called as undefined term.

In geometry the plane is considered as flat surface and the two vectors are used for span the surface. This terms are called linearly independent vectors. The planes are intersected and create the angle is called as dihedral angle.

The nonzero normal vector terms are used to derive the plane equation through the point,

n. ( x – x0 ) = 0 for n = ( a, b ,c ) and X0 = (x0 , y0, z0 )

where X = (x, y, z).This is derive the plane’s general equation as ax + by + cz + d = 0 where d = -ax0 – by0 – cz0.

The distance between the points are calculated as D =  `(d)/(sqrt(a^(2) + b^(2) + c^(2)))` .

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More about plane in geometry


Properties of plane terms in geometry:

In Euclidean space, the parallel planes are present or plane is parallel to the line. Rotation, translation, reflection ans glide reflections are followed in plane motions.

The plane terms in different branches:

A plane which one get the differential structure is called as differential geometry.
The complex analysis is rise the abstraction of complex plane.
If the spherical geometry is taken from a plane means that terms  are called as stereographic projection.

Geometry Terms A Through Z

Introduction to geometry terms a through z

There are number of  terms available in geometry. Learning geometry terms is an essential and an interesting one. The geometry terms are the basis for solving the geometry problems. Without knowing about the geometry terms, we cant able to solve the problems.
The terms of  geometry finds its application also in real life.In this artcle of geometry terms a through z, we are going to learn some of the basic terms involved in geometry.

A through L geometry terms:


Acute angle:  An angle which is greater than 0o but less than 90o is called an acute angle.

Area: The Area of a region is the number of square units that it takes to cover the region.

Angle: An angle is formed by two rays with a common end point called the vertex

Box: A surface which is made up of rectangles.

Collinear Points: If three or more points lie on a line, then the points are called collinear points.

Concurrent lines: If two or more straight lines pass through the same point, then they are called concurrent lines. The point through which the lines pass is known as point of concurrency.

Complementary angles: Two angles are said to be complementary if the sum is equal to 90o

Diameter: A straight line segment that passes through the center of the circle

Equilateral triangle: The triangle having all the sides are equal.

Hexagon : A six sided polygon

Hypotenuse: The side opposite to the right angle in a right triangle.

Intersecting planes: The planes which share a line is referred as Intersecting planes.

Kite: Kite is a quadrilateral which has two distinct pairs of consecutive equilateral side.

Locus: Locus is a set that satisfies the given condition.


M through Z geometry terms:


Mean: The average for the set of given data's.

Mid-Range: The arithmetic mean of maximum value and minimum value given in a data set

Null set: An empty set is called as null set.

Obtuse Angle: An angle which is greater than 90o but less than 180o is called an obtuse angle

Plane: A plane is a set of points on a flat surface that extends without end in all directions.

Parallel lines: The lines that lie in the same plane and never intersect are called as Parallel lines.

Perpendicular lines: If two lines lie in the same plane and intersect at right angles, they are called perpendicular lines.

Quadrilateral: Afour sided polygon such as square,rectangle etc.

Ray: A ray starts from a fixed point and extends endlessly in one direction.

Right Angle: An angle of measure 90o is called a right angle

Straight Angle:An angle of measure 180o is called a straight angle.

Supplementary Angle: The two angles are said to be Supplementary if the sum is equal to180o

Surface Area: The total area of the surface of a solid object

Trapezium: A quadrilateral in which two opposite sides are parallel and two opposite sides are non-parallel

Vertical angles: The angles which share a common vertex and whose sides form two lines

Zero dimensional: The object having no dimension.

Geometry Determining an Angle

Introduction:

In mathematics, an angle is the branch of geometry which is defined as the two rays sharing a common endpoint to form the figure is the vertex of the angle. The amount of rotation is the magnitude of the angle that separates the two rays. For the geometric configuration and its angular magnitude the term "angle" is used. The word angle means "a corner" which is come from Latin. There are different types of angle in geometry.They are Right angle, Straight angles, acute angles, Obtuse angles, Complementary angle, Supplementary angles.


Conditions for determining an angle:


Let as assume the x be the variable for angle. Then,

Right angle

Right angle is the angle in which the value of angle is 90 degree.

If x = 90 degree, it is right angle.

Straight angle

Straight angle has the angle value as 0 degree.

If x = 0 degree, it is straight angle.

Acute angle

When the angle value is below 90 degree then it is acute angle.

If 0 < x < 90 degree, it is acute angle.

Obtuse angle

When the angle value is above 90 degree then it is obtuse angle

If x > 90 degree, it is obtuse angle.

Let as assume x and y are two angles. Then,

Complementary angle

The angles are called as complementary angle when the sum of the two angles is 90 degrees.

If x + y = 90 degree, it is Complementary angle.

Supplementary angle

The angles are called as Supplementary angle when the sum of the two angles is 180 degrees.

If x + y = 180 degree, it is Supplementary angle.

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Examples:


Example 1: find the type of angle for below values?

1. x = 10
2. x = 90
3. x = 300
Solution:

1.  The given value is x = 10 degree.

It satisfy the condition 0 < x < 90.

Therefore, it is an acute angle

2. The given value is x = 90 degree.

It satisfy the condition x = 90.

Therefore, it is right angle.

3. The given value is x = 300 degree.

It satisfy the condition x > 90.

Therefore, it is an obtuse angle

Example 2: Check whether the angles are Complementary angle or Supplementary angles for given data below?

1. x = 30, y = 60

2. x = 80, y = 100

Solution:

1. x = 30, y = 60

x + y = 30 + 60

= 90

Therefore, it is Complementary angle.

2. x = 80, y = 100

x + y = 80 + 100

= 180

Therefore, it is Supplementary angle.

Area of a Kite Geometry

Introduction about kite in geometry:

In geometry a kite, or deltoids, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the sides of equal length are opposite. The two diagonals of a kite are perpendicular and half the product of their lengths is the area of a kite. It has four vertices's. We can calculate the area for many shapes in geometry. In this article we shall discus about how to how to calculate area of kite with geometry example problems.

Source-Wikipedia

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Geometry Formula and example problems:

The space occupied by the kite is called area of kite.

Formula:

Area of kite (A) = half the product of two diagonals.

Let assume,

d1 and d2 are the two diagonal of kite.

Area of kite (A) = (d1 x d2) /2 square unit.

Example problems:

1. Find the area of kite whose diagonal length diagonal (d1) = 20cm and diagonal (d2) = 15cm.

Solution:

Given:

Diagonal (d1) = 20cm

Diagonal (d2) = 15cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (20 x 15) / 2

= 100/2

=50

Area of kite (A) = 50 cm^2

2. Find the area of kite whose diagonal length diagonal (d1) = 12cm and diagonal (d2) = 8cm.

Solution:

Given:

Diagonal (d1) = 12cm

Diagonal (d2) = 8cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (12 x 8) / 2

= 96/2

=48

Area of kite (A) = 48 cm^2

3. Find the area of kite whose diagonal length diagonal (d1) = 25cm and diagonal (d2) = 15cm.

Solution:

Given:

Diagonal (d1) = 25cm

Diagonal (d2) = 15cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (25 x 15) / 2

= 375/2

=187.5

Area of kite (A) = 187.5 cm^2

4. Find the area of kite whose diagonal length diagonal (d1) = 8cm and diagonal (d2) = 6cm.

Solution:

Given:

Diagonal (d1) = 8cm

Diagonal (d2) = 6cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (8 x 6) / 2

= 48/2

=24

Area of kite (A) = 24 cm^2

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Area of kite geometry – practice problem:


1.      Find the area of kite whose diagonal length diagonal (d1) = 12cm and diagonal (d2) = 6cm.

Answer: Area (A) = 36cm^2

2.      Find the area of kite whose diagonal length diagonal (d1) = 18cm and diagonal (d2) = 9 cm.

Answer: Area (A) = 81 cm^2

3.      Find the area of kite whose diagonal length diagonal (d1) = 8cm and diagonal (d2) = 6cm.

Answer: Area (A) = 24 cm^2

What is a Pentagon in Geometry

Introduction to Pentagon in geometry:

Pentagon is the one of the important mathematical figure in geometry.  It is a five sided polygon.  Pentagon is making with the help of 5 sides and 5 angles. Pentagon is classified into following two types.  They are

Regular Pentagon
Irregular pentagon
In this article we have to study about what is pentagon in geometry.


Brief Study about what is a pentagon in geometry?


What is Regular pentagon in geometry?

A pentagon is usually 5 sided figures.  The sides and angles are equal of the pentagon are equal in measure so it is named as regular pentagon.

What is Irregular pentagon in geometry?

Irregular pentagon is also one of the types of pentagon.  Here the sides and angles are not equal in measure.  They are different sides and angles.  So it is named as irregular pentagon.

What is the Pictorial representation of the Regular Pentagon?

What are the Properties of the regular pentagon?

5 sides are equal in measure
5 angles are equal in measure.
Sum of the interior angles measures 540 degree
Each interior angle measures 108 degree
Sum of the exterior angles measures 360 degree
Exterior angle measures 72 degree
Pentagon is formed with the help of three triangles
Pentagon has five lines of reflectional symmetry
Pentagon has five lines of rotational symmetry

What is the area of the regular and irregular pentagon?

The following formula is used to find the area of the regular pentagon,

A=`(1)/(2)` x Apothem X Perimeter

Here A is the area of the pentagon

Apothegm is the radius of the in circle of the pentagon

Perimeter is the sum of all sides of the pentagon

This is the formula to calculate the area of the pentagon.

Geometry Proportions

Introduction of geometry proportions:-

In mathematics, Proportions in arithmetic and geometry, a particular relation between groups of numbers or quantities. In arithmetic, proportions are the equality of ratios; ratio is the division of one number by another. A continued proportions is a property of every three terms in a geometric progression. A proportions is a statement that two ratios are equal such as a:b = c:d.



Example problem for geometry proportions:-


Problem1:

Are the ratios 30g: 40g and 48 kg: 72 kg in geometry proportions?

Solution:

30 g: 40 g =30 / 40 = 3 / 4

= 3: 4

48 kg: 72 kg = 48 / 72 = 4 / 6

= 4: 6           So, 30: 40 = 48: 72.

Therefore, the ratios 30 g: 40 g and 48 kg: 72 kg are in geometry proportions,

i.e. 30 : 40 :: 48 : 72.

The middle terms in this are 40, 48 and the extreme terms are 30, 72.


Problem 2:

Do the ratios 30 cm to 4 m and 20 sec to 5 minutes form a geometry proportions?

Solution:

Ratio of 30 cm to 4 m = 30: 4 × 100 (1 m = 100 cm)

= 3: 40

Ratio of 20 sec to 5 min = 20: 5 × 60 (1 min = 60 sec)

= 20: 300

= 1:15

Since, 3: 40 ≠ 1: 15, therefore, the given ratios do not form a geometry proportions.



Problem 3:

Sam works as a dental hygienist. Last week Sam ade 500 for 20 hours of work How many hours must Sam work in order to make 800?

Solution:

Sam works as a dental hygienist

50020hours=800 / x hours

20 hours * $800 = x hours * $500

16000 = $500 x

16000 / 500 = x

32 = x

Sam 32 hours work in order to make $800

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Practice problems for Geometry proportions problems:        


Problem 1:

Gabriella bought five cantaloupes for 3 How many can taloupes can Shayna buy if she has21?

Answer: 35 gabriella

Problem 2:

If you can buy one can of pineapple chunks for 5 then how many can you buy with 10 ?

Answer: 50 pineapple chunks

Problem 3:

If you can buy four bulbs of elephant garlic for 12 then how many can you buy with 96?

Answer:  8 bulbs

Problem 4:

One package of blueberries costs 6 How many packages of blueberries can you buy for 42?

Answer: 7 blueberries