Question #24916

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Answer 1 · 2018-02-03T06:51:39

The length of AB #=sqrt(AC^2+BC^2)=sqrt(4^2_3^2)=5cm#

If #AD=BE=CF=h# cm be the height of the prism then surface area

#=h(AB+BC+CA)+2DeltaABC#
#=h(5+3+4)+2*1/2*4*3# #cm^2#

#=12h+12# #cm^2#

By the problem

#12h+12=108#

#=>h=8cm#

Now #AF=sqrt(AC^2+CF^2)=sqrt(4^2+8^2)=4sqrt5cm=#

And #BF=sqrt(BC^2+CF^2)=sqrt(3^2+8^2)=sqrt73cm=#

Now three sides of #Delta ABF# are known . So area of the surface #ABF# can be found out using Heron's formula given below

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