In this question , to find the total surface area , we have to find the area of all faces and add them .
And here the base is a hexagon. THe formula of area of hexagon is
[tex] \frac{3 \sqrt 3}{2} a^2 [/tex]
And in the given diagram, side length , a=4cm , so area is
[tex] \frac{3 \sqrt 3}{2} (4)^2 = 24 \sqrt 3 [/tex]
Now we need to find the area of triangle.
We have 6 triangular faces. And for area of triangle, we need the slant edge, and for that we use pythagorean formula
[tex] 8^2+(2 \sqrt 3)^2=h^2
\\
h^2 =76
\\
h = 2 \sqrt{19} [/tex]
Now we use the formula of area of triangle which is half times the product of base times height. And since there are 6 triangles, so we have to multiply by 6 too.
[tex] =6*(1/2)*4*2 \sqrt{19} = 104.61 [/tex]
So total surface area is
[tex] 24 \sqrt 3 + 104.61 =146.2 cm^2 [/tex]
