Getting a Container inside an Expanded inside a Row to expand vertically to fit the space available in the Row - flutter

Question

I have a row containing four Expanded widgets. Its code looks as follows:
Row(
children: [
Expanded(
child: Container(
width: double.infinity,
color: Colors.blueGrey,
padding: const EdgeInsets.all(10),
child: (Text(
lessonData.language,
style: const TextStyle(
color: Colors.white,
),
)),
),
),
Expanded(
flex: 1,
child: Container(
width: double.infinity,
color: Colors.blueGrey,
padding: const EdgeInsets.all(10),
child: (Text(
lessonData.cEFRLevelName,
style: const TextStyle(
color: Colors.white,
),
)),
),
),
Expanded(
flex: 1,
child: Container(
width: double.infinity,
color: Colors.blueGrey,
padding: const EdgeInsets.all(10),
child: (Text(
lessonData.lessonTopic,
style: const TextStyle(
color: Colors.white,
),
)),
),
),
Expanded(
child: Container(
width: double.infinity,
color: Colors.blueGrey,
padding: const EdgeInsets.all(10),
child: (
Text(
lessonData.lessonHeading,
style: const TextStyle(
color: Colors.white,
),
)),
),
)
],
),
The resulting display is unsatisfactory if any of the texts in the Containers inside the Expanded widgets are forced to wrap. As in this image:
Click here to display an image of my problem when text has wrapped in one Container but not in the other three.
This image shows something like what I'd like the Row to look like.
I simply can't get the Container widgets containing text without any wrap to expand out to the height of the row.
Among other candidate solutions, I've tried setting the height to double.infinity and double.maxFinite, setting Constraints in the Containers to Constraints: BoxConstraints.expand(). All these options either do nothing or generate an error on hot reload.
I'm reluctant to try an IntrinsicHeight widget because I'm warned that it's very hungry.
I'd be very grateful for any solution and/or comment you might have!
TIA
Jaime

Answer 1

If I understood what you want, I may have a suggestion. It's more of a workaround, but you can move the Container with the colored backgroud up a level and remove each other Container, making the new Container the parent of the whole Row: I put the code in a DartPad, and this is how it looks.
Just an excerpt of the code:
Container(color: Colors.red,child: Row(
children: [
Expanded(...),
Expanded(...),
//and so on...
This works only on an aesthetic level: each Text will still get resized, but you won't notice.