Question

Question #24916

Answer 1

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