How to you calculate area of square whose diagonal length is 8cm?

Firstly you need to work out the length of a side.

Using Pythagorian Theorum for a right angled triangle

a²+b²=c² where a = the length, b = height & c = diagonal

since c = 8 and a = b are the same

2a² = 64
a² = 32
a = 5.657 cm

since the area of the square is a² then area = 32cm²