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
And in the given diagram, side length , a=4cm , so area is
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
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.
So total surface area is
