how to write parquet files in java with apache arrow

I am trying to write data in java into apache parquet. So far, what i've done is use apache arrow via the examples here: https://arrow.apache.org/cookbook/java/schema.html#creating-fields and create an arrow format dataset.

Question is, how do I write it into parquet after that? Also, do I need to use apache arrow to output the data as a parquet file? or can I use apache parquet directly to serialize the data and then output it as a parquet file?

what i've done:

try (BufferAllocator allocator = new RootAllocator()) {
    Field name = new Field("name", FieldType.nullable(new ArrowType.Utf8()), null);
    Field age = new Field("age", FieldType.nullable(new ArrowType.Int(32, true)), null);
    Schema schemaPerson = new Schema(asList(name, age));
    try(
        VectorSchemaRoot vectorSchemaRoot = VectorSchemaRoot.create(schemaPerson, allocator)
    ){
        VarCharVector nameVector = (VarCharVector) vectorSchemaRoot.getVector("name");
        nameVector.allocateNew(3);
        nameVector.set(0, "David".getBytes());
        nameVector.set(1, "Gladis".getBytes());
        nameVector.set(2, "Juan".getBytes());
        IntVector ageVector = (IntVector) vectorSchemaRoot.getVector("age");
        ageVector.allocateNew(3);
        ageVector.set(0, 10);
        ageVector.set(1, 20);
        ageVector.set(2, 30);
        vectorSchemaRoot.setRowCount(3);
        File file = new File("randon_access_to_file.arrow");
        try (
            FileOutputStream fileOutputStream = new FileOutputStream(file);
            ArrowFileWriter writer = new ArrowFileWriter(vectorSchemaRoot, null, fileOutputStream.getChannel())
        ) {
            writer.start();
            writer.writeBatch();
            writer.end();
            System.out.println("Record batches written: " + writer.getRecordBlocks().size() + ". Number of rows written: " + vectorSchemaRoot.getRowCount());
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}

but this outputs as an arrow file. not a parquet. Any ideas how I can output this to parquet file instead? And do i need arrow to generate a parquet file to begin with - or can i just use parquet directly?