Let's create a Custom View called SquareLayout
public class SquareLayout extends LinearLayout {
    public SquareLayout(Context context) {
        super(context);
    }
    public SquareLayout(Context context, AttributeSet attrs) {
        super(context, attrs);
    }
    @Override
    protected void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
        super.onMeasure(widthMeasureSpec, widthMeasureSpec);
    }
}
Use it in the layout as follows.
<LinearLayout
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:orientation="horizontal">
    <com.your-package.SquareLayout
        android:layout_width="0dp"
        android:layout_height="match_parent"
        android:layout_weight="1">
        <Button
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:background="@drawable/something_item1" />
    </com.your-package.SquareLayout>
    <com.your-package.SquareLayout
        android:layout_width="0dp"
        android:layout_height="match_parent"
        android:layout_weight="1"
        android:layout_marginLeft="15dp">
        <Button
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:background="@drawable/something_item2" />
    </com.your-package.SquareLayout>
    <com.your-package.SquareLayout
        android:layout_width="0dp"
        android:layout_height="match_parent"
        android:layout_weight="1"
        android:layout_marginLeft="15dp">
        <Button
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:background="@drawable/something_item3" />
    </com.your-package.SquareLayout>
    <com.your-package.SquareLayout
        android:layout_width="0dp"
        android:layout_height="match_parent"
        android:layout_weight="1"
        android:layout_marginLeft="15dp">
        <Button
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:background="@drawable/something_item4" />
    </com.your-package.SquareLayout>
</LinearLayout>
I was able to arrange four square buttons like this.
The original was stackoverflow here.