Pentagonal Pyramid

Pyramid is a solid whose base is a planar polygon with a triangular face on each side. These triangular faces meet in a point which is not in the plane fo the base. Pentagonal pyramid is pyramid whose base is a pentagon, and having 5 triangular faces on each side.

 Pentagonal Pyramid Formula:
 Let,   a = apothem length, s,b = side, h = height and l = slant height,

• Area of Base(A) = `(5/2)axxs`
• Surface Area of Pyramid = `(5/2) a xx s + (5/2) s xx l = A + (5/2) s xx l`
•  Volume of Pyramid = `(5/6) axxbxxh`

Properties of pentagonal pyramid:

• A pentagonal pyramid has 6 faces. One base and 5 lateral faces
• A pentagonal pyramid has 10 edges
• A pentagonal pyramid has 6 corners

 

Examples on pentagonal pyramid:

1) Find  volume and surface area of a pentagonal pyramid with the given apothem length 7, side 8, height 9 and the slant height 10.
 Solution:   a = 7, s = b = 8, h = 9, l = 10

  Step 1:  Area of the base(A) = `(5/2) axx s`                                 
                                               = 2.5 * 7 * 8
                                               = 2.5 * 56
                                               = 140

  Step 2:  Surface Area of Pyramid = `A + (5/2) s xxl`
                                                       = 140 + ((5/2) * 8 * 10
                                                       = 140 + (2.5 * 80)
                                                       = 140 + 200
                                                       = 340

  Step 4: Volume of Pyramid =`(5/6) a xx b xxh`
                                              =  `(5/6)` * 7 * 8 * 9
                                              = (0.833) * 56*9
                                              = 0.8333 * 504
                                                = 419.98

2) Find the surface area a pentagonal pyramid with the given apothem length 2.5, side 5 and the slant height 9.
 Solution:   a = 2.5, s = b = 5, , l = 9

       Area of the base(A) = `(5/2)axxs`                         
                                          = 2.5 * 2.5 * 5
                                          = 6.25 * 5
                                          = 31.25
    Surface Area of Pyramid = `A + (5/2) s xxl`
                                               = 31.25 + ((5/2) *5 * 9
                                               = 31.25 + (2.5 * 45)
                                               = 31.25+ 112.5
                                               = 143.75

Algebra is widely used in day to day activities watch out for my forthcoming posts on Mean Median Mode Definition and icse syllabus 2013. I am sure they will be helpful.

Pictures of pentagonal pyramid

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