The area of a parallelogram is equal to area of a rectangle on the same base and between same parallels. In fact, a rectangle is also a parallelogram. We may replace the parallelogram by rectangle and proceed in the same way to prove the corollary.
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IFMpi82YwRMQAAGgIGiCpizBsgIkBGoxiyT/htgIN0wYM4aiFNGwIECYKCoFdp6rR7OfrnrCOhgQcYIAAJJN/Vqjw8YSC8MuOsI6GDBuIwRcCDAeQYGgIG8CrhBQMcIcPdBQKBao0zD74CBdMKAGwR0jIANdx90zL3SZ2AgrxWGc+Vt61bMrgHqCAACaTB0L8cIDKQPBsyuAdvrCJSCA2AAGBikACCA8XsxxbT+FhhIFwwkDQQUFICBQVZo67V6OPtl1hEgIwAYpNXcKz1uYCA9MGDWEYh7RsDJGAADwEBWgY77BygxzNRBpg5WGQPAQDpgoKPjxViVGHaMvpxnYAAYkK5N26kjUKUJVHoFyfeTmW0BBpIPA11dO2NdR6AUEAADKYcBs7IgXQPJNCsgJNjzCgwkGwbMyoJJ6RpwAwIwkGIYcE8fpI5AsGaBGSdbX2AguTDgnj4Y5zoCbuPP9xoYSCkMuEGAOgLJNipAJPjzCwwkEwbcIBD3OgL5AMD9HjCQQhgwQYCugeDNAkNOtsbAQPJgwASBJHYNAAMpBABncqI5fZB7DSTbpICQcM4vMJAsGDCnD8bxXgNuoy/nNZmBFIEBBYXCMQYMOH06AwPJgYEkFhQCBlJk9M6Vf6FnEwTICKTPsICU4M45MJAMGDBBIA0ZAQcUyAykABiYPhicCWCwaKsxAAzEHwbSMH3QMf58z8BAwmHAHCxIRgDzAmD8jwFgIN4wYA4WTFNGwAEDYCDBMGCCALMG/DcBjBVNyQwkCwSSPmvAMX/zGRhIKAyYIEBGANMCXIKLATID8QQCMgLvIgEwkEAY0HsNtE7olXFN/aIFhcgIBGcCGCzakhmIJwjovQZaW7dJU9OAaEGhtGYEHBwABhIGA3r3wbbJW7IgoCWGFy3t5U503ISIGAg4BsgMxAsI9O6DbW29WRDQEsMrVz7reGJqn4GBBMGAOX1w8fI+TCBgEyAzQGaAzEC8QMCcPrhmzXOpBQD3gQMDCYEBs7IgXQOYFKASXgyQGYgHEJiVBdPeNQAMJAQAnAJDZkYAEAjPBDBctCYzEB8QaGnpZ4yAmwBcr8kMxBwMzFkDgADmBKCEHwNkBuwGAnPWABkBFwW88xIYiDEMAALhN/oYLZrniwFgwF4YAASGGn++d4CBmMIAXQOYUj5T4r1o4gIYsBMGzMGCZATyYUDuPWAghjDQuf5paclQRwDji8b40H2o7sCAfTDQ2fmyMEagsPmbnwADMYMB7RpwCgpRR2Boo4xRoUkUMQAM2AUD2jXgFBSijoBp+/n/BgZiBAPm9EHqCGB8URgf2xwad8CAPTBgTh+kjkB+8zffBQZiAgPujICWGOZeA0MbZEwKTaKKAWDADhhwZwS0xHAa7z5omny5fwMDMYABHSOQmbiVew1QTZCKkpbGADAQPQzoGIFMpo86AuW6v/E9YMByGDBnDZAR4Oo3qqtftls49oCBaGHAnDVARsBw+jL+BAYshgF3HQEdLMgYgcKNMUaFNlHGADAQHQy46wjoYEHGCJTh/Hm+AgxYCgNuENAxAtx9ELOL0uzYdvH4AwaigQE3COgYAe4+mMfly3wLGLAQBsyuAUoMF2+IMSr0iToGgIHwYcDsGqCgUJmuX+BrwIBlMAAIYGxRGxvbrzwGgYFwYQAQKODoHt4GBiyCAbOOABmByhtljAzNoogBYCA8GDDrCJAR8EAArp8CA5bAQMf9A5QYtnTaWBTmwjbjBTXAQDgw0NHxIiWGXQbu50tgwAIY6Nq0nToCgAA1BGIcA8BA8DDQ1bWTOgJ+ur+xLmAgYhgwKwvSNRCvK0Ku4DlfGgPAQLAwYFYWpGvAcHIf/gQGIoQB9/RB6ghgKoBFfGMAGAgOBtzTB6kj4IPrF1gFMBARDLhBgDoC8TUBDJxzR2YgHBCgjkABF/fpbWAgAhgwQYCuAQwFqIh3DJAZ8B8I3BkBBQG6Bnxy/QKrAQZChgFz+iD3Goi3CWDinD8yA/6DgDl9kHsNFHBwH98GBkKEAQoKYRzAQzJjgMyAf0BAQSEfHb6CVQEDIcGACQJkBJJpCph9Os8rMOAPDJggQEagAjf3+FVgIAQYYPpgOg0CMEjPeQcGvMMA0wc9urnHnwMDAcOAOViQjEB6DAIYSM+5Bga8wYA5WJCMgEdnr+LnwECAMGCCALMG0mMOgEC6zjUwUD0MmCDArIEqnNyHnwADAcGACQJkBNJlDsBAus43MFAdDJggQEbAB1evchXAQAAwoPcaaJ3QK+Oa+kULCpERSJcxAALpO9/AQOUwoPcaaG3dJk1NA0IdgSod3MefAQM+w4DefbBt8pYsCGiJ4UVLe7kBTYxvQIOxp8/YqznnwEBlMKB3H2xr682CgJYYXrnyWR9tjVVVowAw4CMMmNMHFy/vAwQAAWIgBTEADJQPA+b0wTVrnqvGu/iNzwoAAz7BgFlZkK4BriirucLkN/GMG2CgPBgwKwsyWNBnR/ewOmDABxgwMwKAQDwbdIyY81ZtDAADpWHAzAgAAh6cO4CfAgMeYcCcNQAIYCjVGgq/i2/sAAPFYcCcNQAIBODmHlcJDHiAAUAgvo03xsu58zMGgIHCMAAIeHTpkH4ODFQJA3QNYCZ+mgnrinc8AQP5YYCugZCc3IfNAANVwEDn+qelJUMdAQws3gbG+fPv/AEDQ2Ggs/NlaWnpp46AD0YdxiqAgQphQLsGnIJC1BHwrzHFmNAyzjEADAyGAe0acAoKUUcgDCv3vg1goAIYMKcPUkcAA4uzgbHv/sUvMPAuDJjTB6kj4N2ow1gDMFAmDLgzAlpimHsN+NeQYkpoGfcYAAZyMODOCGiJYe41EIaN+7MNYKAMGNAxApmJW7nXQAoqycXdlNj/aMAKGBDRMQKZTB9jBPzx5tDXAgyUgAFz1gAZgWgaW0wO3W2OgbTDgDlrgIxA6F7ueYPAQBEYcNcR0MGCjBHAkGw2JPYtuvhMMwy46wjoYEHGCHj25UhWAAwUgAE3COgYAe4+GF1Di8mhve0xkFYYcIOAjhHg7oOR+LgvGwUG8sCA2TVAiWHMyHYzYv+ijdE0woDZNUCJYV88ObKVAAMGDAAC0TaqmBr6xzEG0gYDgEBknh3YhoEBFwyYdQTICGBMcTQm9jn8uE0TDJh1BMgIBObPoa4YGHgHBjruH6DEMFMHBSMN30iToHlaYKCj40VKDIdq0eFtDBiQ3dK1aTt1BAABQIAYqDoG0gADXV07qSMQnjeHvqXUw4BZWZCuAa4Mk3ClyjGEG8dJhwGzsiBdA6F7deAbTDUMuKcPUkcg3MYTs0LvJMVAkmHAPX2QOgKBe3JkG0gtDLhBgDoCGFOSjIljCT+ekwoDbhCgjkBkPh3KhlMJAyYI0DUQfuOJYaF5kmIgiTBgggBdA6F4cmQbSR0MmNMHudcAppQkU+JYoonnpMGAOX2Qew1E5tGhbThVMEBBoWgaSgwK3ZMeA0mCAQoKhea/Vm0oNTBgggAZAQwq6QbF8YUX40mBARMEyAhY5deB7kwqYIDpg+E1ihgQWqcxBpIAA0wfDNRrrV954mHAHCxIRgCzSqNZcczBxn3cYcAcLEhGwHrv9n0HEw0DJggwayDYBhHDQd+0xkCcYcAEAWYN+O6zsVhhYmHABAEyAhhVWo2K4w4+9uMKAyYIkBGIhW8HspOJhAG910DrhF4Z19QvWlCIjEDwjSGGg8ZpjoE4woDea6C1dZs0NQ2IFhQiIxCIx8ZmpYmDAb37YNvkLVkQ0BLDi5b2Vn3zkTQ3bhw75k4MlB8DcYMBvftgW1tvFgS0xPDKlc/GxrTY0WAUSBQMmNMHFy/vAwS4Ex0xQAwEHgNxggFz+uCaNc8F4y6sNVYKJAYGzMqCdA2Uf1XDFSBaEQPeYiAuMGBWFqRrIFZ+HejOJgIGzIwAIOCtYcMY0I8YqCwG4gADZkYAEAjUW2O38tjDgDlrABCorBGj0UcvYsB7DNgOA+asAUAgdl4d+A7HGgYAAe+NGEaAhsSA9xiwGQYAgcB9NBEbiC0M0DXgvQHDBNCQGPAnBmyFAboGEuHToRxELGGgc/3T0pKhjgANuT8NOTqio9cYsBEGOjtflpaWfuoIhGKl8d9I7GBAuwacgkLUEaAR99qI83tiyI8YsA0GtGvAKShEHYH4G3UYRxArGDCnD1JHgIbcj4acdRBHXmPAJhgwpw9SRyAMK43/NmIDA+6MgJYY5l4DNOBeG3B+Twz5FQO2wIA7I6AlhrnXQPxNOqwjiAUM6BiBzMSt3GuASnKBV5LzyxxYT7pAwwYY0DECmUwfYwTCcs+Ebcd6GDBnDZARSFcji6lyvuMQA1HDgDlrgIxAwpw6hMOxGgbcdQR0sCBjBDCGOBgD+5i+OI0SBtx1BHSwIGMEQnDOBG7CWhhwg4COEeDug+lrYDFVznlcYiAqGHCDgI4R4O6DCXTpkA7JShgwuwYoMYwpxMUU2M90xmoUMGB2DVBiOCTXTOhmrIMBQCCdjSkmynmPcwyEDQOAQEIdOcLDsgoGzDoCZAQwiDgbBPuenvgNEwbMOgJkBCJ00ARt2hoY6Lh/gBLDTB1k6iAxEMsYCAsGOjpepMRwggzYpkOxAga6Nm2njgAmEEsT4Oo/PVf/xc51GDDQ1bWTOgI2uWfC9iVyGDArC9I1QONarNHlM+LDxhgIGgbMyoJ0DSTMiS04nEhhwD19kDoCNPI2NvLsE3FZTgwECQPu6YPUEbDANRO6C2XBwNj+sTKmf4xsfnWzb8s1d/xEGlu2HCgxTB0BGt1yGl2+Q5x4jYFtO1+Wrh09vi7/9tAFUt/XIGO3Ncru3eLb4gYB6ggk1IUtOaySMPDhn35YanpqZHjPcJlzxxxfluM+PV9q6rtl+MgNMrZpi9A1QAPvtYHn98RQuTFwzU9vllnfnuvrklk5UYb31EhNz6GBgQBdA5a4ZkJ3oyQMzH1g7gEYmHXrLPG6TP30pVJT/5AMG7lBakZ3y38ufYCBYwweJAaIgdBi4KoHlsjMZbNlxs2zfFua78jIsMeHZ4HAj8yAOX2Qew0k1IEtOqyKYKDrN13iZfmv29dKQ/PjUjfmcRk+qlumfPIz2VRduUTP97j6IwaIAa8x4IaBu/p+In4sR6+Z6hsMUFDIIodM0a5UBAM73toh1S7L1j4qTeO3SkNjn9Q3Pi5HXnJZNk2nfXde/3PzewyCGCAGyo0BBwbOXXGBbHzhWV+W999zhi8wYIIAGYEUuXHEhxoKDCxds16aM1uyIDCueat85ut3Z9Nz2m8HDNCIl9uI8z1ixY8YsBUGmD4YsRumfPOBw4CCgJMRUBC4evmj2bSc9tcBAzTufjTurIM4qiQGbIQBc9YAGYGUO3MEhx8oDJggcNXNG7IpOe2jAwZowCtpwPku8eJXDNgGAyYIMGsgAidkkxIYDJggoBkBp38OGKBh96thZz3EUqUxYBMMmCBARgBXjkqBQGDgzoc2Dxoj4GQEgAEa7kobbr5PzPgdA7bAgN5roLV1mzQ1DYgWFCIjEJUNsl1VwHcYWL7uUWmd9Hh2sOCYcX2ycPH/HsgIAAM07H437KyPmKo0BmyAAb37YFtbbxYEtMTwypXP4kgoEKkCvsKAe/qgDhb88jfXDwEBBQK6CWjAK23A+T4x41cMRA0D5vTBNWuei9QE2DgKqAK+wYCCgHv6oNk14GQFgAEadb8addZDLFUTA1HCgFlZkK4BjNgWBXyBATMjUAwEgAEa8GoacH5D3PgVA1HBgJkRAARssUH2QxXwDAPmrIFSIAAM0Kj71aizHmKpmhiIAgbMWQOAAAZsmwKeYKAaEAAGaMCracD5DXHjVwyEDQOAgG22x/7kU6BqGDBBwF1HQA2/2MIAQhp2vxp21kMsVRoDYcKACQLUEchnQ7xngwIlYeBDaz8kw1YNk2HfHSYDrw1kb1RkjhGoBATIDNB4V9p4831ixs8YCAIGTlh9qhyyUtvJ4fLKK/tEb2NsjhEABGywPPahkAIFYdX3ENkAAAZFSURBVOCpp56S6dNnyrCaQ6Vx0lQZPX6S1NaNkg/ObZfGlk0HbjpUKQgAAzTsfjbsrIt4qjQG/ISBVfffK8ee8H45pOZQGfdOO1lXVy/nnDNfmpu3HCgoBAgUsiDet0WBvDDQ09Mjo0ePk/PP/4FcffU+ufZayS5XXrlLjjjiPDnssOlSP7ZHyhksmK+7gG4CGvBKG3C+T8z4FQN+wcDydd+TulENcv753y/QTp4mTU1PUFnQFrdjP4oqMAQG9u7dK83NE+SSS7oPQIADA87zkUdeIO879WNFxwXkgwDnPWCAht2vhp31EEuVxoAfMPDgU73SMG580XbyqKMukDPPvLRoA8yHKGCLAkNgYPXq1TJtWntBEFAg0AzBiNpR8sivflEVEAADNOCVNuB8n5jxKwb8gIErv/F1OXbq+SXbSe0y2Ldvny3tPfuBAgUVGAID557bLu3t64oGuQLB6IYpcvBxt8rBp3V7Wt4z42FhQQNigBgIKwa8tln6+5rGmWW1k21tx4mOv+KBArYrMAQGZs6cLfPmbSwJAy2ZD8jBx97oCQT0P1VYDQDbwWyIAWJAY8APGDh07KlltZNTppwlOgaLBwrYrsAQGFi48Esya9Z1RWFABxUOq6mTzMULZeL8RVUvkz79VXnf525iQQNigBgILQamXHF91W2W097VT50hHzxzccl2sra2Xvbs2WO7D7B/KDC0HHF/f780NEwYNDrWGTjoPF944Y9k2rQTkQ8FUAAFUqkA7WQqT3uiD3pIZkCP9rLLLpejj56dFwjmz++RxsYJov8ZeKAACqBAWhWgnUzrmU/mceeFgf3792eBQDME2mWgYwguuujHctJJ82Ts2Bbp7u5OphocFQqgAAqUqQDtZJlC8bVYKJAXBpw9X79+vegYAh1UOGfOR+WGG5bIrl27nI95RgEUQIHUK0A7mfoQSIQARWEgEUfIQaAACqAACqAAChRVABgoKg8fogAKoAAKoEDyFQAGkn+OOUIUQAEUQAEUKKrAIBj45z9Fbrghd1Mifda/eaAACqAACqAACiRbgUEw8Ktf5UDAqSfw3HPJPniODgVQAAVQAAVQQAYXHVq3LgcDDz6Ye77nHiRCARRAARRAARRIugIHMgN/+YvIddeJfPObue6BpUtFvvENkb/+NekScHwogAIogAIokG4FDsDAL36RywY88EBOkIceyv3NDbfSHSAcPQqgAAqgQPIVOAADHR058//tb3MH/fLLub+/973ki8ARogAKoAAKoECaFcjCwFtv5Yz/xhtF/vWvd+X41rdy7+vnPFAABVAABQYr4Ay2dj/rTKzvf1/kpZcGf5e/UMBmBbIw8POf50zfvOXAI4/k3t+61eZDYN9QAAVQIBoF3BCQ7/Urr0SzX2wVBSpVIAsDK1fmTN8M3J07c+/r5zxQAAVQAAUGK+AAgPvd/ftFHn4413ZqhoAHCsRBgYNeey0XtE5QF3p+/fU4HA77iAIogALhKeC0l+YWFQj0s+uvNz/hbxSwU4GDHnusPBjYuNHOA2CvUAAFUCAqBQrBgFZv1c9uvjmqPWO7KFCZAgctX54L2jfeyP/DP/wh9/ktt+T/nHdRAAVQIK0K5IOBf/xDRMdf6WebNqVVGY47bgocpAGr0wqLPdasyQW2jiHggQIogAIokFPAgYF8zwoE7tlZaIYCNiuQhYFnnim+izt25GDAnG1Q/Fd8igIogALJViAfBDjv3XWXCBdQyT7/STq6g266qTS9av+Xfs+sQ5AkITgWFEABFKhUAcf43b97+22R7dtz7aV+Tr0Btzq8tlWBAxUIbd1B9gsFUAAFbFUgHww4+6rVXPXz73zHeYdnFLBXAWDA3nPDnqEACliuQDEY0F3Xz/WGbzxQwHYFgAHbzxD7hwIoYK0CxWBAZ2jp53oHWB4oYLsCwIDtZ4j9QwEUsFaBQjDwpz+J6E3e9PMHH7R299kxFDigADBwQApeoAAKoEBlCjgwUOhZB13v3VvZOvk2CkShADAQhepsEwVQIBEK5IOA664TWbYslxF4881EHCYHkQIFgIEUnGQOEQVQAAVQAAWKKQAMFFOHz1AABVAABVAgBQoAAyk4yRwiCqAACqAAChRTABgopg6foQAKoAAKoEAKFPh/1PiOmYfH0XMAAAAASUVORK5CYII=[/img][br]Area of a parallelogram = base x height[br]In the figure DA is the altitude of both the rectangle ABCD and the parallelogram ABEF.[br]Now, area of parallelogram ABEF = Area of rectangle ABCD[br] = AB x DA[br][math] \therefore [/math] Area of parallelogram = base x height.[br]
Parallelograms on the [color=#ff0000]equal base[/color] and between the same parallels are equal in area.