Question

如图，菱形ABCD的对角线AC和BD相交于点O，求证：S菱形ABCD=12AC?BD

如图，菱形ABCD的对角线AC和BD相交于点O，求证：S菱形ABCD=12AC?BD．

Answer 1

证明：∵菱形ABCD的对角线AC和BD相交于点O，
∴AC⊥BD，
∴S_菱形ABCD=S_△ACD+S_△ABC=

1

2

AC?OD+

1

2

AC?OB=

1

2

AC（OB+OD）=

1

2

AC?BD．