Question

Show that Area of rohmbus is half the product of the length of its diagonal

Answer 1

Answer:

Step-by-step explanation:

consider two diagonals AC and BD

diagonals of a rhombus intersect at O. i.e. OB⊥AC and OD⊥AC

Area of rhombus ABCD = Area of Δ ABC +Area of Δ ADC

                                         = (1/2 x AC x OB) + (1/2 x AC x OD)

                                          = 1/2 x AC x (OB + OD)

                                         = 1/2 x AC x BD

        Area of rhombus   = 1/2 x product of length of diagonals

Note: area of triangle = 1/2 bh

           OB + OD = BD