Show that area of rhombus is half the product of its diagonals .

Asked by Vikas | 16th Jan, 2018, 11:50: PM

Expert Answer:

 
begin mathsize 16px style Diagonals space of space straight a space rhombus space intersect space at space right space angles.
rightwards double arrow OB perpendicular AC space and space OD perpendicular AC
Area space left parenthesis rhombus space ABCD right parenthesis equals Area space left parenthesis triangle ABC right parenthesis plus Area space left parenthesis triangle ADC right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times AC cross times OB plus 1 half cross times AC cross times OD
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times AC cross times left parenthesis OB plus OD right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times AC cross times BD
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times Product space of space diagonals end style

Answered by Rashmi Khot | 17th Jan, 2018, 09:26: AM