Question 1113945
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The area of the base is easy -- {{{6*8=48}}} sq cm.<br>
There are two triangular faces with base length 8; the altitude of each of those triangular faces is the hypotenuse of a right triangle with legs 3 and 4; that hypotenuse has length 5.  So we have two triangles each with area {{{(1/2)(8)(5) = 20}}} sq cm.<br>
The other two triangular faces have base length 6; the altitude of each of them is the hypotenuse of a right triangle with legs 4 and 4; that hypotenuse has length 4*sqrt(2).  So we have two triangles each with area {{{(1/2)(6)(4*sqrt(2)) = 12*sqrt(2)}}}.<br>
The total surface area is then
{{{48 + 2(20) + 2(12*sqrt(2)) = 88+24*sqrt(2)}}}