Question

Find find the area of a quadrilateral one of whose diagonal is 40 cm and the length of the perpendiculars drawn from the opposite verticals on the diagonal are 16 cm and 12 cm

Answer 1

Let ABCD be a quadilateral.Diagonal, AC=40 cmBL⊥AC, such that BL=16 cmDM⊥AC, such that DM=12 cmArea of the quadilateral=(Area of ∆DAC)+(Area of ∆ACB)

                                       =[(12×AC×DM)+(12×AC×BL)] cm2=[(12×40×12)+(12×40×16)] cm2=(240+320) cm2=560 cm2

Hence, the area of the quadilateral is 560 cm2.