Write a C# solution using stack, the code is written based on the java code - segmentfault blog.

Leetcode84_LargestRectangleInHistogram.cs

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Leetcode84_LargestRectangleHistogram
{
    /// <summary>
    /// Leetcode 84 - largest rectangle histogram
    /// code practice is based on the coding blog:
    /// https://gist.github.com/jianminchen/74f27e22b520c6074c1fbc6e5c45d9a4
    /// 
    /// </summary>
    class Program
    {
        static void Main(string[] args)
        {
            RunTestcase(); 
        }

        public static void RunTestcase()
        {
            var area = CalculateLargestRectangleArea(new int[]{2, 1, 5, 6, 2, 3});
            Debug.Assert(area == 10);
        }

        /// <summary>
        /// greedy algorithm to calculate the largest rectangle histogram
        /// 
        /// </summary>
        /// <param name="height"></param>
        /// <returns></returns>
        public static int CalculateLargestRectangleArea(int[] height) // [2, 1, 5, 6, 2, 3]
        {
            var stack = new Stack<int>();

            var index = 0;
            var largestArea = 0;

            int length = height.Length; // 6

            while (index < length) // true; index = 1; index = 2;
            { 
                //     stack empty            going upward
                if (stack.Count == 0 || height[stack.Peek()] < height[index]) // index = 1, false;
                {
                    stack.Push(index++); // 0, index = 1;
                }
                else
                {
                    // going downward and then pop stack, calculate rectangle.
                    popStackAndCalculate(ref largestArea, stack, height, index);
                }
            }

            while (stack.Count > 0)
            {
                popStackAndCalculate(ref largestArea, stack, height, length);
            }

            return largestArea;
        }

        /// <summary>
        /// downward and then pop stack to calculate the rectangle
        /// </summary>
        /// <param name="largestArea"></param>
        /// <param name="stack"></param>
        /// <param name="height"></param>
        private static void popStackAndCalculate(ref int largestArea, Stack<int> stack, int[] height, int rightIndex)
        {
            int length = height.Length; // 6

            int lastHeight = height[stack.Pop()]; // 2
            int width = stack.Count == 0 ? rightIndex : rightIndex - stack.Peek() - 1; // 1

            largestArea = Math.Max(largestArea, lastHeight * width); // 2 * 1
        }
    }
}