![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/77094b36acaf2edd16ecc3588e1001e939019366?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
解:设这个长方形ABCD的长为a厘米,宽为b厘米.即BC=a,AB=b,
则其面积为ab平方厘米.
∵E为AD的中点,F为CE的中点,
∴过F作FG⊥CD,FQ⊥BC且分别交CD于G、BC于Q,则FQ=
CD=
b,FG=
a.
∵△BFC的面积=
BC?FQ=
a?
b,
同理△FCD的面积=
?b?
a,
∴△BDF的面积=△BCD的面积-(△BFC的面积+△CDF的面积),
即:6=
ab-(
ab+
ab)=
ab
∴ab=48.
∴长方形ABCD的面积是48平方厘米.
故答案为:48.