You use the sine rule.
Diagonal / sin90 = width / sin30
5 / 1 = width / 0.5
5 = width / 0.5
width = 0.5 * 5
width = 2.5 cm
Diagonal / sin90 = length / sin60
5 / 1 = length / (sqrt(3) / 2)
5 = length / (sqrt(3) / 2)
length = 5 * (sqrt(3) / 2)
length = 5sqrt(3) / 2 cm
Area
= length * width
= 5sqrt(3) / 2 * 2.5
= 25sqrt(3) / 4 cm^2
Perimeter
= 2*length + 2*width
= 2(5sqrt(3) / 2) + 2(25sqrt(3) / 4)
= 5sqrt(3) + (25sqrt(3) / 2)
= (10sqrt(3) / 2) + (25sqrt(3) / 2)
= 35sqrt(3) / 2 cm