Pyramid Geometry – Surface Area and Volume Formulas :: Danielitte

Convex Quadrilateral

Segment of Circle

Sector of Circle

Regular Poligon of N Sides

Sperical Segment

Sperical Sector

Frustum of Right Circular Cone

Triangular Prism

Arithmetic Progression

Geometric Progression

Decimal Logarithm

Natural Logarithm

Euler's Formula

Trigonometric Functions For A Right Triangle

Trigonometric Table

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Formulas With T=tan(x/2)

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Sides And Angles Of A Plane Triangle

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Trigonometric Equation Cos

Trigonometric Equation Sin

Trigonometric Equation Tan

Trigonometric Equation Cotan

Linear Inequation

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Logarithmic Inequation

Trigonometric Inequation Cos

Trigonometric Inequation Sin

Trigonometric Inequation Tan

Trigonometric Inequation Cotan

Horizontal Shifting

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Equation of Line

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Equation of Line Joining Two Points A,B

Equation of Sphere Center at M and Radius R in Rectangular Coordinates

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Hyperboloid of One Sheets

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Geometry - Pyramid

Pyramid

Understanding Pyramid in Geometry: Definition, Properties, and Key Formulas

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that converge to a single point called the apex. Pyramids are widely studied in geometry for their unique structure and practical applications, such as in architecture and art.

Diagram of a square showing side length, diagonal, and perimeter.

Key Properties of a Pyramid

Base: The base can be any polygon (triangle, square, rectangle, etc.).
Faces: The triangular faces connect the edges of the base to the apex. The number of triangular faces equals the number of sides of the base.
Apex: The topmost point of the pyramid where all triangular faces meet.
Height \(h\): The perpendicular distance from the apex to the center of the base.

Key Formulas for a Pyramid

1. Volume \(V\):

The volume of a pyramid measures the amount of space it occupies:

\[ V = \frac{Ah}{3} \]

Where

\(A\): Area of the base
\(h\): Perpendicular height of the pyramid

2. Base Area \(A\):

The base area depends on the shape of the base. For example:

If the base is a square: \(A = a^z\), where \(a\) is the side length
If the base is a triangle: \(A = \frac{1}{2} b h_b \) where \(b\) is the base and \(h_b\) is the height of the triangle.

Applications of Pyramids

Architecture: Famous structures like the Egyptian pyramids and modern architectural designs use pyramidal shapes for stability and aesthetics.
Mathematics: Essential for understanding volume and surface area in geometry.
Engineering: Used in structural design and analysis for weight distribution.