The actual area of the triangle reflected in the front view is 2×2÷2=2, and there is a triangle behind it.

The actual area of the triangle reflected in the side view is 2×(√3)÷2=√3.

The other side of the face reflected from the side view is also an isosceles triangle, and the waist length is the hypotenuse of the right triangle reflected from the front view =√8, so the height of the triangle =√7, so the actual area of the triangle is 2×(√7)÷2=√7.

The actual area of the square reflected in the top view is 2×2=4.

Therefore, the required surface area = sum of the above areas = 2× 2+(√ 3)+(√ 7)+4 = 8+(√ 3)+√ 7 =12.3778.