Question

What is the area of a rhombus with: Side=8 cm Acute angle between one pair is 30

Answer 1

Length of one diagonal = 2×8sin15∘=16sin15∘2×8sin⁡15∘=16sin⁡15∘

Length of the other diagonal = 2×8cos15∘=16cos15∘2×8cos⁡15∘=16cos⁡15∘

Then, area of the rhombus = 12×12× product of lengths diagonals

=12×16sin15∘×16cos15∘=128sin15∘cos15∘=64sin30∘=12×16sin⁡15∘×16cos⁡15∘=128sin⁡15∘cos⁡15∘=64sin⁡30∘

= 32 sq cm