Question 747026


the lateral surface area of a regular pyramid is L.S.A {{{pyramid=(1/2)p*l}}} where{{{ p}}} represents the perimeter of the base and {{{l}}} the slant height

{{{cube =6s^2}}} where {{{s }}}= length of the side

Maria needs to paint all of the lateral surfaces of the shed, including the roof but not including the floor:

so, she will need L.S.A {{{pyramid=(1/2)p*l}}} and {{{cube =4s^2}}}  since she doesn’t  need bottom and top of cube (both are inside shed)

L.S.A {{{pyramid=(1/2)p*l}}} ...{{{p=4*12=48}}}  and the slant height {{{l}}} will be hypothenuse of right triangle formed by the hight {{{h=20-12=8}}} of pyramid and half of the side length of the base  {{{12/2=6}}}
{{{l^2=8^2+6^2}}}
{{{l^2=64+36}}}
{{{l^2=100}}}
{{{l=10}}}
L.S.A {{{pyramid=(1/2)48*10 }}}
L.S.A {{{pyramid=48*5}}}
L.S.A {{{pyramid=240ft^2}}}

and {{{cube=4s^2=4*12^2=4*144=576ft^2}}}

so, total surface area is:  {{{240ft^2+576ft^2=816ft^2}}}