Mathematics Question and Solution
a² = 4²+4²-2*4*4cos120
a² = 32+16
a² = 48
a = 4√(3) cm.
b²+(0.5a²) = 4²
b² = 16-12
b = √(4)
b = 2 cm.
Or
cos60 = b/4
½ = b/4
b = 2 cm.
Therefore, total surface area of the hexagonal based prism is;
2(area rectangle with length 4√(3) cm and width 4 cm)+4(area triangle with base 4√(3) cm and height 2 cm)+6(area rectangle with length 12 cm and width 4 cm)
= 2(4√(3)*4)+4(½*4√(3)*2)+6(12*4)
= 32√(3)+16√(3)+288
= 288+48√(3)
= 48(6+√(3)) cm²
= 371.1384387633 cm²
