Question 1198369
 
{{{a=RS = (5/8)m=62.5cm }}}
{{{b=QR = (3/8)m= 37.5cm }}}
 {{{VS = (2/3)m=66.67cm }}}



to find the height of pyramid, first  find the diagonal  of the base

{{{d^2=a^2+b^2}}}
{{{d^2= (62.5cm)^2+(37.5cm)^2}}}
{{{d^2= 5310cm^2}}}
{{{d = sqrt(5310cm^2)}}}
{{{d = 72.87cm}}}


then

{{{d/2 =(72.87cm)/2}}}

{{{d/2 =36.435cm}}}


and, height  is

{{{h^2=(66.67cm)^2-(36.435cm)^2 }}} 

{{{h^2=3117cm^2}}}

{{{h=sqrt(3117cm^2)}}}

{{{h=55.8cm}}}



The formula for calculating the surface area of the pyramid is:


{{{SA=ab+a*sqrt( (b/2)^2 +h^2)+b*sqrt((a/2)^2 +h^2)}}}
 
{{{SA=62.5cm *37.5cm +62.5cm*sqrt( (37.5cm/2)^2 +(55.8cm)^2)+37.5cm* sqrt((62.5cm /2)^2 +(55.8cm)^2)}}}

{{{SA=2344cm^2 +3679cm^2 +2398cm^2}}}

{{{SA=8421cm^2 }}}


answer: total surface area is  {{{8421cm^2}}}