Edit in JSFiddle

/* This menu container will decide the 
dimensions such as height, width and margin for the menu.
The width in this will help to create the verical menu.
*/
#menucontainer {
    margin: 0px;
    padding: 0px;
    width: 120px;
    height: 160px;

        display: block;
}
/* This will set the backgorund and the position for the menu
*/
#menucontainer ul {
    list-style: none;
    position: relative;
    display: inline-block;
        background-color:#2CDF7B;
    padding: 0px;
    top: -16px;
    border-radius: 5px;
    -moz-border-radius: 5px;
    -webkit-border-radius: 5px;
}
/* This will form the single menu
its float: left will help to create the menu
*/

#menucontainer ul li {

    list-style: none;
    margin: 0px;
    padding: 0px;
    height: 35px;
    width: 100%;
    position: relative;
    display: inline;
    float: left;
}
/*
This will set the anchor for single menu.
background transperant and text-decoration none
*/
#menucontainer ul li a {
    list-style: none;
    top: 5px;
    margin-left: 10px;
    padding-left: 10px;
    margin-right: 10px;
    padding-right: 10px;
    background-color:transparent;
    position: relative;
    display: inline;
    text-decoration: none;
    font-family:"Times New Roman", "Arabic";
    font-size: 20px;
    color:grey;
    font-weight: bold;
}

/* The following selector will define the 
way menu should be displayed when mouse is hovering above it.
*/
#menucontainer ul li:hover {
    list-style: none;
    background-color:rgba(44, 223, 123, 0.3);
    position: relative;
    display: inline;
    box-shadow: 0px 0px 9px rgba(0, 0, 0, 0.6);
    border-radius: 5px;
    -moz-border-radius: 5px;
    -webkit-border-radius: 5px;
    -moz-box-shadow: 0px 0px 9px rgba(0, 0, 0, 0.4);
    box-shadow: 0px 0px 9px rgba(0, 0, 0, 0.4);
    -webkit-box-shadow: 0px 0px 9px rgba(0, 0, 0, 0.4);
}
#menucontainer ul li:hover > a {
    list-style: none;
    margin-left: 10px;
    padding-left: 10px;
    margin-right: 10px;
    padding-right: 10px;
    background-color:transparent;
    position: relative;
    display: inline;
    text-decoration: none;
    font-family:"Times New Roman", "Arabic";
    font-size: 20px;
    color:white;
    font-weight: bold;
    border-radius: 5px;
}

#menucontainer ul li > a:hover {
    list-style: none;
    margin-left: 10px;
    padding-left: 10px;
    margin-right: 10px;
    padding-right: 10px;
    background-color:transparent;
    position: relative;
    display: inline;
    text-decoration: none;
    font-family:"Times New Roman", "Arabic";
    font-size: 20px;
    color:white;
    font-weight: bold;
    border-radius: 5px;
}


/* The following selector will create Arrow displayed on the right 
hand side of the base menu when the mouse is hovering above it.
*/

#menucontainer ul li:hover:after {
  content: "";
    display: block;
    border: 15px solid transparent;

    border-left-color: #2CDF7B;
    position: absolute;
    bottom: 2%;
    left: 100%;
    
}