解答:解:如图,四边形ABCD是菱形,BD,AC分别是其对角线且BD=6,AC=8,求其面积和周长.∵四边形ABCD是菱形,BD,AC分别是其对角线,∴BD⊥AC,BO=OD=3cm,AO=CO=4cm,∴AB=5cm,∴菱形的周长=5×4=20cm;S菱形=12×6×8=24cm2.故本题答案为:20cm;24cm2.