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

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 =

$\frac{32}{4} cm = 8cm$

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,

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

$\Rightarrow h= \sqrt{9} = \pm 3 cm$

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

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