# The perimeter of square base pyramid and its slant height 32 cm and 5 cm respectively. find its height.

2
by ab12

2014-09-18T15:40:05+05:30

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so length of each side of square base is 32/4 = 8 cm
slant height=5 cm
so h² = (slant h)² - (base/2)² = 5² - (8/2)².
so h
² = 9
h = +3 and h= -3
but distance cannot be negative so take the positive one
so h = 3 cm

2014-09-18T21:27:59+05:30

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See diagram for understanding structure of a pyramid.

perimeter of base = 32 cm
The side of square at the base = 32/4 = 8 cm = 2a in the diagram

Slant height  L is the distance between middle of a side at the base and the top of the pyramid.  L = 5 cm  = AB

Vertical Height of pyramid = h    it is the distance between center O of base square and top of pyramid A.

Half of a side of base square = 8/2 = 4 cm = a  = OB = OC

Applying Pythagoras theorem :  h² + a² = L²

h² = 5² - 4² = 9

h = Vertical Height of the Pyramid = 3 cm

i hope it is easy to understand.
This indicates that slant height from one corner of the square base to the vertex of the pyramid is greater than slant height taken from middle of the side of the square base. If it so, the point from slant height is taken should be specified. Will you please clear this doubt ? i am simply curious.