The total surface area is the sum of the areas of the four triangular faces.
Three of them have a base of 10 and a height of 6.7. The fourth has a base of 10 and a height of 8.7. Here, we'll show the sum in one expression, so we can do some simplification.
A = ∑(1/2)bh = (1/2)(10)(6.7) +(1/2)(10)(6.7) +(1/2)(10)(6.7) +(1/2)(10)(8.7)