This is summer homework that's due in 2 days!

Split the surface area into geometric shapes as shown in the figure below.

Top part
The area of one triangle is
A₁ = (1/2)*(10 cm)*(4 cm) = 20 cm²
There are 3 of these triangles.

Vertical sides..
The area of one vertical side is
A₂ = (10 cm)*(6 cm) = 60 cm²
There 3 of them.

Bottom part
The triangle is equilateral with each side  = 10 cm, and each angle = 60 deg.
The area is (from the Law of Sines)  equal to
A₃ = (1/2)(10 cm)*(10 cm)*sin(60) = 43.3 cm²

The total surface area is
3A₁ + 3A₂ + A₃
= 3*20 + 3*60 + 4.3
= 283.3 cm²

The surface area is  283.3 cm²