The median Bay Area home price surged to an all-time high of $820,00 in March, up 9.3 percent from February and up 14.7 percent from March of last year, research firm CoreLogic reported Tuesday. The previous peak was $784,000 in November. The report includes newly built and existing homes and condos sold in all nine counties. For the past six months, the median price has risen 12.8 percent year-over-year on average.