Geometry Definition, Formulas, and Shapes: What Is It?

The oldest area of mathematics, geometry, is concerned with the dimensions, size, forms, and angles of objects. The topics covered by geometry are those that are relevant to daily life. Shapes in geometry can be either two-dimensional or three dimensional, or both. Flatforms are 2D shapes in in-plane geometry, including triangles, squares, rectangles, and circles. Three-dimensional forms like a cube, cuboids, cones, etc. are also referred to as solids in solid geometry. The fundamental building blocks of geometry are points, lines, and planes, which are a subset of coordinate geometry. We are giving you comprehensive knowledge of geometry, geometry forms, and geometry formulae on this page. Candidates will be better able to resolve geometry-related issues if they are familiar with the subject. If you are preparing for competitive exams and looking for expert guidance, you can download our General Knowledge Free Ebook Download Now.

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Table Of Content

• Dimensional Definition
• What are the Different Geometric Branches?
• Geometry of Planes (2D Geometry)
• Geometric Angles
• Different Angles
• Polygons
• Types of Polygons
• Formulas for Geometry

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Dimensional Definition

The phrases "geometry" and "metron," which refer to measuring and the Earth respectively, are derivations of Ancient Greek. In terms of distance, form, size, and the relative placement of objects, geometry is concerned with the qualities of space. The fundamental concepts of geometry primarily rely on points, lines, angles, and planes.

 

What are the Different Geometric Branches?

The following are the branches of geometry:

• Geometry in algebra
• Simple geometry
• Geometry that differs
• Geometry in Euclid
• Convex geometry
• Topology

 

Geometry of Planes (2D Geometry)

Flat, paper-drawable forms are referred to as plane geometry. These consist of two-dimensional lines, circles, and triangles. Two-dimensional geometry is another name for plane geometry. Squares, triangles, rectangles, circles, and lines are examples of 2D geometry. The characteristics of the 2D forms below are provided to you in this section.

Point

A point is an area or position on a plane. Typically, a dot stands in for them. It's crucial to realize that a point is a location rather than a thing. The point is the lone place and has no dimensions.

Line

The line has no thickness, is perfectly straight with no bends, and goes on forever in both directions.

Geometric Angles

Angles are created when two lines, referred to as rays, cross at the same location. It is referred to as the angle's vertex.

Different Angles

1. An acute angle is a smaller angle than a straight angle, ranging from 0 to 90 degrees.
2. Obtuse Angle: Obtuse angles are those that are more than 90 degrees but less than 180 degrees.
3. A right angle is a 90-degree angle.
4. Straight Angle - A straight angle is the angle created by a straight line, and it has a degree of 180.

 

Polygons

Any form figure with at least three sides and three vertices is referred to as a polygon. The words "poly" and "gon" both imply "many" and "angle," respectively. Consequently, polygons have a lot of angles. The type of a polygon determines its area and boundary. The figures of sides and vertices are said to serve as the foundation for the distribution of polygons.

Types of Polygons

The many kinds of polygons are:

• Triangles
• Quadrilaterals
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon

In the table below, we've described the attribute as well as given instances of polygons with those features. Candidates can use these graphs to assist them in studying geometry questions on various competitive examinations.
 

Triangle	a triangle with three sides whose internal angle total is always 180 degrees.	The three sides and angles of an equilateral triangle are equal. Two equal sides and angles make up an isosceles triangle. The three uneven sides and angles make up a scalene triangle.
Quadrilateral	A quadrilateral polygon has four sides, four edges, and four vertices. The total of its internal angles is 360 degrees.	The vertices of a square are at right angles and have four equal sides. The sides and angles of a rectangle are equal and at right angles. Two sets of parallel sides make up a parallelogram. The opposing sides and angles are of equal size. All four sides of the rhombus are the same length. They do not, however, have an interior angle of 90 degrees. One set of opposing sides of a trapezium must be parallel.
Pentagon	A plane figure with five straight sides and five angles	–
Hexagon	A plane figure with six straight sides and six angles	–
Heptagon	A plane figure with seven sides and seven angles	–
Octagon	A plane figure with eight straight sides and eight angles.	–
Nonagon	A plane figure with nine straight sides and nine angles.	–
Decagon	A plane figure with ten straight sides and ten angles.	–

Formulas for Geometry

Every figure and shape in geometry has a unique formula for calculating its area and perimeter. Applicants must complete the many geometry-related problems in the Quantitative Aptitude part of competitive examinations. Below is a table listing all the key geometry formulae.
 

Shape	Area	Perimeter
Rectangle (l= Length and b= breadth)	(l*b)	2(l+b)
Square (a is the side of the square)	a2	4a
Triangle (a,b and c are sides of the triangle)	1/2 (b × h)	a + b +c
Circle (r = radius)	πr2	2πr (Circumference of Circle)
Parallelogram (a = side, b=base,h=vertical height)	A = b × h	P = 2(a+b)

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A triangle's area is equal to 1/2(b h).