Question

cho hinh thang abcd co duong cheo ac bd cat nhau tai o ab=12cm cd=24cm Saod=12cm2 tinh S abcd
giup minh nha mn

 

Answer 1

ABCD là hình thang

=>\(S_{AOD}=S_{BOC}\)

=>\(S_{BOC}=12\left(cm^2\right)\)

Xét ΔOAB và ΔOCD có

\(\widehat{OAB}=\widehat{OCD}\)(hai góc so le trong, AB//CD)

\(\widehat{AOB}=\widehat{COD}\)(hai góc đối đỉnh)

Do đó: ΔOAB~ΔOCD

=>\(\dfrac{OA}{OC}=\dfrac{OB}{OD}==\dfrac{AB}{CD}=\dfrac{1}{2}\)

OA/OC=1/2

=>\(S_{AOB}=\dfrac{1}{2}\cdot S_{BOC}=\dfrac{1}{2}\cdot12=6\left(cm^2\right)\)

ΔOAB~ΔOCD

=>\(\dfrac{S_{OAB}}{S_{OCD}}=\left(\dfrac{AB}{CD}\right)^2=\dfrac{1}{4}\)

=>\(S_{COD}=6\cdot4=24\left(cm^2\right)\)

Diện tích hình thang ABCD là:

24+6+12+12=30+24=54(cm²)