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Pyramid Calculator

A Pyramid is a solid object having a polygon base, triangular sides that meet at the top. A Pyramid is a three-dimensional structure and a polyhedron.

Calculate the area, perimeter of Pyramid (Pyramid Calculator)

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Table of Contents:

    Formula

    Triangular Pyramid
    Area of the base (A) = ½ * a * s
    Surface Area of Pyramid = A + ((3/2) sl)
    Volume of Pyramid = (1/6) abh
    Where,
    a= apothem length
    s= side length
    sl= slant height
    abh area of base * height

     

    Square
    Area of the base (A) [s²]
    Surface Area of Pyramid = [s² + 2sl]
    Volume of Pyramid = [(1/3)b²h ]
    Where,
    s= side length
    sl= slant height
    b= base
    h= height

    Pentagonal
    Area of Base : [(5/2)as]
    Surface Area of Pyramid : [ (5/2)as + (5/2)sl ]
    Volume of Pyramid : [ (5/6)abh]
    Where,
    As = area of side length
    sl= slant height
    abh area of base * height

    Hexagonal
    Area of Base: [(6/2) as]
    Surface Area of Pyramid: [3as + 3sl]
    Volume of Pyramid: [abh ]
    Where,
    As = area of side length
    sl= slant height
    abh area of base * height

    A pyramid is a polyhedron with one face as base, a polygon and all the other faces triangles meeting at a common polygon vertex as the apex. It is a structure where the upper surfaces are triangular and converge on one point.

    Examples: Surface area and volume of a triangular pyramid calculator
     

    Find the area, surface area and volume of a triangular pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

    Step 1: Find the area of the base.
    Area of the base (A) = ½ * a * s = 0.5 * 2 * 3 = 3.

    Step 2: Find the surface area of pyramid.
    Surface Area of Pyramid = A + ((3/2) sl) = 3 + ((3/2) * 3 * 5) = 3 + (1.5 * 15) = 3 + 22.5 = 25.5.

    Step 3: Find the volume of pyramid.
    Volume of Pyramid = (1/6) abh = (1/6) * 2 * 3 * 4 = 0.17 * 24 = 4.08.

    Find the area, surface area and volume of a right square (right rectangular) pyramid with the given side length3, height 4 and the slant height 5.

    Step 1: Find the area of the base. (right rectangular pyramid calc: find a)
    Area of the base (A) [s²] = 32  = 9

    Step 2: Find the surface area of pyramid.
    Surface Area of Pyramid = [s² + 2sl] = 32 +2*5= 9+10 = 9 +2*5*3 =9+30 = 39

    Step 3: Find the volume of pyramid. (right rectangular pyramid calc: find v)
    Volume of Pyramid = [(1/3)b²h ] = [(1/3)*92 *4] = (1/3)*9*4 = 36/3 = 12

    Find the area, surface area and volume of a Pentagonal pyramid with the given side apothem length 2, side 3, Slant height 4 and height 5.

    Step 1: Find the area of the base.
    Area of Base : [(5/2)as] = [ (5/2)2*3]= 5/2*6= 2.5*6= 15

    Find the surface area of pyramid.
    Surface Area of Pyramid : [ (5/2)as + (5/2)sl ]= 15+(2.5*3*4) = 15+ (2.5*12) =15+30 = 45

    Find the volume of pyramid.
    Volume of Pyramid : [ (5/6)abh] = (5/6) 2*3*5=  (5/6) * 30 = 0.833 *30 = 25 \

    Find the area, surface area and volume of a Hexagonal pyramid with the given side apothem length 2, side 3, Slant height 4 and height 5.

    Step 1: Find the area of the base. Area of Base:  [(6/2) as] = [(6/2) 2*3= (6/2) *6 = 3*6 = 18

    Find the surface area of pyramid.
    Surface Area of Pyramid:  [3as + 3sl] = [(3*2*3) + (3*3*4)] = 18+36 = 54

    Find the volume of pyramid.
    Volume of Pyramid:  [abh ] = 2*3*5 = 30