hexagon from https://www.flutterclutter.dev/

main.dart

import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        body: Center(
          child: CustomPaint(
            painter: MyPainter(),
            child: Container(
              height: 500,
              width: 500,
            ),
          ),
        ),
      ),
    );
  }
}

class MyPainter extends CustomPainter {
  @override
  void paint(Canvas canvas, Size size) {
    Paint paint = Paint();
    Path path = Path();

    final double width = size.width;
    final double height = size.height;
    final double halfSize = size.width / 2;
    final double radius = size.width * 0.04;
    final double halfRadius = size.width * 0.02;
    final double startHeight = height * 0.01;
    final double oneFifthSize = size.width / 5;

    // Path number 1

    paint.color = Color(0xff00AEC7);
    path = Path();
    path.lineTo(halfSize - radius, startHeight);
    path.cubicTo(halfSize - halfRadius, 0, halfSize + halfRadius, 0,
        halfSize + radius, startHeight);

    path.cubicTo(halfSize + radius, startHeight, width - radius,
        oneFifthSize + halfRadius, width - radius, oneFifthSize + halfRadius);

    path.cubicTo(width - halfRadius, height * 0.24, width, height * 0.26, width,
        height * 0.29);

    path.cubicTo(
        width, height * 0.29, width, height * 0.71, width, height * 0.71);

    path.cubicTo(width, height * 0.74, width * 0.98, height * 0.77,
        width * 0.96, height * 0.78);

    path.cubicTo(width * 0.96, height * 0.78, width * 0.54, height,
        width * 0.54, height * 0.99);

    path.cubicTo(width * 0.52, height, width * 0.48, height, width * 0.46,
        height * 0.99);

    path.cubicTo(width * 0.46, height, width * 0.04, height * 0.78,
        width * 0.04, height * 0.78);

    path.cubicTo(
        width * 0.02, height * 0.77, 0, height * 0.74, 0, height * 0.71);

    path.cubicTo(0, height * 0.71, 0, height * 0.29, 0, height * 0.29);

    path.cubicTo(0, height * 0.26, width * 0.02, height * 0.24, width * 0.04,
        height * 0.22);

    path.cubicTo(width * 0.04, height * 0.22, width * 0.46, height * 0.01,
        width * 0.46, height * 0.01);

    path.cubicTo(width * 0.46, height * 0.01, width * 0.46, height * 0.01,
        width * 0.46, height * 0.01);

    canvas.drawPath(path, paint);
  }

  @override
  bool shouldRepaint(CustomPainter oldDelegate) {
    return true;
  }
}