activity

@Override
public void onMenuToggle(final boolean isOpen) {
    setBackgroundDimming(isOpen);
}

private void setBackgroundDimming(boolean dimmed) {
    final float targetAlpha = dimmed ? 1f : 0;
    final int endVisibility = dimmed ? View.VISIBLE : View.GONE;
    mDimmerView.setVisibility(View.VISIBLE);
    mDimmerView.animate()
            .alpha(targetAlpha)
            .setDuration(DIM_ANIMATION_DURATION)
            .withEndAction(new Runnable() {
                @Override
                public void run() {
                    mDimmerView.setVisibility(endVisibility);
                }
            })
            .start();
}

@OnClick(R.id.dimmer_view)
protected void dimmedBackgroundClicked(View sender) {
    mFloatingActionMenu.close(true);
}

layout

<FrameLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    xmlns:fab="http://schemas.android.com/apk/res-auto"
    android:id="@+id/content_root"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:foreground="@drawable/header_shadow">

    <View
        android:id="@+id/dimmer_view"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:background="#80ffffff"
        android:alpha="0"
        android:visibility="gone"/>

    <com.github.clans.fab.FloatingActionMenu
        android:id="@+id/fab"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:layout_gravity="bottom|right"
        android:layout_marginBottom="8dp"
        android:layout_marginRight="8dp"
        fab:menu_fab_size="normal">

        <com.github.clans.fab.FloatingActionButton
            style="@style/Rombe.Widget.FloatingActionButton"/>

        <com.github.clans.fab.FloatingActionButton
            style="@style/Rombe.Widget.FloatingActionButton"/>
    </com.github.clans.fab.FloatingActionMenu>

</FrameLayout>