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

Answers (1)

The hieght of the square pyramid is 3 cm. Let's see how we solve and claculate this height - 

Let a = Length of slant height  = 5 cms

       h = Height of the square pyramid

       b = Half of the length of the sides of square base.

 

Now perimeter of the square base is given as = 32 cm

So length of the side of the square base = 

                                                                    frac324 cm = 8cm

 

Now a = 5 cm (Given)

         h = To find

         b=  (8/2) cm = 4 cm

 

In the right angle triangle shown in the image of square pyramid, we can use Pythagorus theorum -

\ a^2 = h^2 + b^2 \ Rightarrow h^2 = a^2 - b^2

Putting the values, we will get,

Rightarrow h^2 = 5^2 - 4^2 = 9

Rightarrow h= sqrt9 = pm 3 cm

 

Now the length cannot be negative so the length of the height of the square pyramid  =  3 cm

 

 

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