Posted by **Joe** on Saturday, February 11, 2012 at 2:27am.

OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid, the volume of the pyramid, and the total surface area of the pyramid by first drawing the net of the pyramid.

- Mathematics -
**Anonymous**, Saturday, February 11, 2012 at 4:31am
sqrt ( 15 ^ 2 - 12 ^ 2 ) = sqrt ( 225 -144 ) = sqrt ( 81 ) = 9 cm

- Mathematics -
**Reiny**, Saturday, February 11, 2012 at 8:34am
Draw one of the side triangles, and consider its altitude from the base of 12, call that x

x^2 + 6^2 = 15^2

x^2 = 19

x =√189

so the surface area = the base + 4triangles

= 144 + 4(1/2)(12)(√189) = ....

for the volume , we need the height of the pyramid,

call it h

h^2 + 6^2 = (√189)^2

h^2 = 153

h = √153

volume = (1/3)(base)(height)

= (1/3)(144)(√153

= 48√153

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