A rectangular prism has 6 sides.
Top side and Bottom side have the same area.
Right side and Left side have the same area.
Front side and back side have the same area.
Area of Top and Bottom = 2 (Length x width)
Area of Top and Bottom = 2 (5x3)
Area of Top and Bottom = 30 cm²
Area of Right and Left = 2 (width x height)
Area of Right and Left = 2 (3 x h)
Area of Right and Left = 6h cm²
Area of Front and Back = 2 (length x height)
Area of Front and Back = 2 (5 x h)
Area of Front and Back = 10h cm²
Total surface area = 30 + 6h + 10h
Total surface area = 30 + 16h cm²
Given that the Total surface are is 62cm²
30 + 16h = 62
16h = 62 - 30
16h = 32
h = 32 ÷ 16
h = 2cm