{"id":358,"date":"2019-11-26T00:08:36","date_gmt":"2019-11-26T00:08:36","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=358"},"modified":"2020-10-15T00:12:07","modified_gmt":"2020-10-15T00:12:07","slug":"solution-to-november-25-2019%e2%80%b2s-challenge","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=358","title":{"rendered":"Solution to November 25, 2019\u2032s Challenge"},"content":{"rendered":"\n
By connecting various points in the figure, we have the following:<\/p>\n\n\n\n
<\/figure><\/div>\n\n\n\n
It is obvious that the radius of each quarter circle is $\\dfrac{\\sqrt{2}}{2}$, and the area of two green regions is:\n$$\\dfrac{1}{2}-\\dfrac{1}{4}\\cdot\\pi\\cdot(\\dfrac{\\sqrt{2}}{2})^2=\\dfrac{1}{2}-\\dfrac{\\pi}{8}$$\nTherefore, the total area of the blue regions is equal to the area of the unit square minus 4 times of the area of the two green regions: \n$$1-4\\cdot(\\dfrac{1}{2}-\\dfrac{\\pi}{8})=\\dfrac{\\pi}{2}-1$$\n<\/p>\n","protected":false},"excerpt":{"rendered":"
![\"\"](\"https:\/\/mathfun4kids.com\/mlog\/wp-content\/uploads\/2020\/10\/Screen-Shot-2019-11-25-at-11.21.33-AM.png\")
<\/figure><\/div>\n\n\n\n