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Let the base of the triangle be x:-

If: 0.5*4*x*6.75 = 81

Then: x = (81*2)/(4*6.75) = 6

Using Pythagoras' the 2 hypotenuse's of the isosceles triangle are 5 cm which are in fact 2 joined right angle triangles

Surface area: 2(0.5*6*4)+ 2(5*6.75)+(6*6.75) = 348 square cm

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Q: What is the surface area of an isosceles triangular prism that has a length of 6.75 cm and a height of 4 cm with a volume of 81 cubic cm?
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