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    You are at:Home»Pure Math»Geometry»Pyramid Geometry Formulas and Properties | Frustum of Pyramid
    Pyramid Geometry Formulas and Properties | Surface area and Volume

    Pyramid Geometry Formulas and Properties | Frustum of Pyramid

    0
    By sivaalluri on July 10, 2022 Geometry

    In this article, we can learn about types of pyramids, geometrical formulas for surface area and volume, and their properties.

    A pyramid is a three-dimensional solid shape that can have any polygon as its base. Its edges converge at a single vertex or apex.

    Its dimensions are defined by the dimensions of the polygon at its base and the length of its lateral edges, which lead to the vertex.

    Table of Contents

    Toggle
    • Types of Pyramids
      • Basic Pyramid Geometrical formulas
      • Triangular Pyramid
      • Square Pyramid
      • Pentagonal Pyramid
      • Frustum of Pyramid

    Types of Pyramids

    Triangular pyramid, Square pyramid &  Pentagonal pyramid

    The type of the pyramid is called according to its base.

    The base is triangle type, then it is called Triangular pyramid.

    If the base is square, then it is called Square pyramid.

    If the base is pentagonal type then it is called Pentagonal pyramid.

    Types of pyramids and geometrical formulas of surface area and volume and its properties. Triangular pyramid, Square pyramid &  Pentagonal pyramid pentagonal pyramid surface area and volume formula and properties | surface area and volume

    Perimeter of a pyramid (p) : It is the distance around the base of the pyramid.

    Slant height of a pyramid ( l) :  It is a diagonal height from the vertex to center one of the base edges.

    Height/Altitude of pyramid ( h) : Altitude ( h) is the perpendicular distance between the apex and bases of a pyramid.

    Right Pyramid & Oblique Pyramid

    Right Pyramid – The Vertex or apex of the pyramid is directly above the center of its base; then, it is called the right pyramid.

    i.e the apex line is perpendicular to the center point of its base.

    The square pyramid and triangular pyramid are examples of right pyramids.

    Oblique Pyramid –  If the Vertex or apex of the pyramid is not directly above the center of its base, then it is called an Oblique pyramid. The face of the oblique pyramid is not congruent.

    Right Pyramid & Oblique Pyramid formula | volume and surface area of a pyramid formula | Pyramid Geometry Formulas

    Basic Pyramid Geometrical formulas

    Slant surface or lateral surface area of the pyramid (S)

     S = \frac{1}{2} \times \text{Perimeter of the Base} \times \text{Slant Height}

    Total surface area of the pyramid (SA)

    SA = Lateral surface area of the pyramid + Base area of pyramid

    Volume of the pyramid (V)

     V = \frac{1}{3} \times \text{Area of the base} \times \text{Height}

     

    Triangular Pyramid

    A triangular pyramid is a  polyhedron with a triangular base and the three faces of the triangular pyramid meet at a point known as apex. The triangular pyramid has

    A triangular pyramid has one triangular base and three triangular faces, Six edges & Four vertices

    The base, faces, edges and vertices are the same for an irregular triangular pyramid or a regular triangular pyramid.

     

    Surface area and volume of a triangular pyramid | Pyramid Geometry Formulas

    Here,

    Height of the triangular pyramid – h

    Slant height of the triangular pyramid – s

    Base length of the triangular pyramid – a

    Surface area and volume of a triangular pyramid

    Base Area of a Triangular Pyramid 

     A = \frac{1}{2} \times a \times b

    Surface Area of a Triangular Pyramid (SA)

    SA = Base Area + 1/2 (Perimeter × Slant Height)

     SA = A + \frac{1}{2} \ (3a + s)

    Volume of a Triangular Pyramid (V)

    V =   1/3 x Base Area×Height

     V = \frac{1}{3} A h

     V = \frac{1}{6} abh

    Square Pyramid

    A square pyramid is square based three-dimensional geometrical figure. All four sides are triangular and they meet at one single point known as the apex.

    square pyramid surface area and volume formula and properties | Pyramid Geometry Formulas

    A Square  pyramid has

    a) Five Faces
    b) Four Side Faces are Triangles
    c) Square Base
    d) Five Vertices (corner points)
    e) Eight Edges

    Base Area of the square pyramid (A)

    A = a2

    Slant surface or lateral surface area of the pyramid (S)

    S= 1/2 x 4a x s = 2as

    Surface area of square pyramid (SA)

    SA = a2 +2as

    The volume of a Square Pyramid (V)

     V = \frac{1}{3} a^3 h

    Where ” s ” is the slant height, “a” is the base length, and “h” is the height the of the square pyramid

    Pentagonal Pyramid

    A pentagonal pyramid is a pyramid with a pentagonal base.

    A Pentagonal pyramid has

    Five triangular face

    Pentagonal base
    Six Faces
    Six Vertices (corner points)
    Ten Edges

     pentagonal pyramid surface area and volume formula and properties | Pyramid Geometry Formulas

    Volume of a pentagonal pyramid (V)

     V = \frac{1}{3} \times \text{Area of the pentagonal base} \times \text{height}

     V = \frac{5}{6} \times a \times b \times h

    Surface Area of a Pentagonal Pyramid (SA)

    SA = 5/2 × a(b + s)

     SA = 1.72 \ a^2 + \frac{5}{2} \ a \ h

     

    Hexagonal Pyramid – A hexagonal pyramid is a pyramid having a hexagonal base. It has a total of 6 sides and 6 triangular lateral faces. A hexagonal pyramid is also known as heptahedron.

    Pyramid name Faces Edges Vertices
     Triangular Pyramid (or) Tetrahedron 4 6 4
     Square Pyramid 5 8 5
     Pentagonal Pyramid 6 10 6
     Hexagonal Pyramid 7 12 7
     Heptagonal Pyramid 8 14 8
     Octagonal Pyramid 9 16 9

    Frustum of Pyramid

    When a pyramid is cut the left over part is called the frustum of a pyramid

    Pyramid Geometry Formulas | Frustum of a pyramid formula surface area volume

    Slant surface of the frustum of a pyramid (S)

    S = 1/2 x sum of perimeter of the ends x slant height

    The volume of the frustum of a pyramid (V)

     V = \frac{h}{3} \left[A_1 + (A_1A_2)^2 + A_2\right]

    Where ‘h’ is the height or thickness A1 & A2 are the areas of the ends of the pyramid

    Related Articles:

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    Centroid of the triangle formula with examples

    Cone formulas  – Surface Area and Volume

    Surface Area and Volume of a Prism Formulas

    Cylinder Formulas – Volume and Surface Area

    Sphere, Hemisphere, Hollow Sphere Formulas – Surface Area and Volume

    Cube and cuboid

    Circle formulas in math

    Quadrilateral formula for area and perimeter

    Triangle Area Formulas

    Formulas for Arc, Perimeter, Segment of circle

    Frustum of a pyramid Geometry Pentagonal pyramid Square pyramid surface area of a pyramid Triangular pyramid Volume of a pyramid formula
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