FÓRMULA DE HERON

[justify]Na maioria das situações, usamos as medidas da base e da altura de um triângulo para calcular a sua área. Contudo, há diversas maneiras de calcular a área de um triângulo, sendo que a escolha é feita de acordo com os dados conhecidos no problema.[/justify][center][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPEAAAC7CAYAAAC0CHgDAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAEDrSURBVHhe7Z0HnFxl1f/PbN90Qg0KBAUhQEIREgLSRAmiFJEiCH+B9+UTEbDgC774+bwvCmIDg1RjlCJKQMpLR0BpCoQaSkA60mvapu7Ozs79n++5c2bvTmbL7M7OzszeX3L23rn1Kef3nPPUmwgUEiNGjIpFTWYbI0aMCkVM4hgxKhwxiWPEqHDEJI4Ro8IRkzhGjApHTOIYMSocMYljxKhwxCSOEaPCEQ/26AFp6ZDF8r40SK3UtzVJ+8JFsqpluWyw2VYS1NZIKiESpNOSDtKSSNRITY0ea09Jc0Nz5gkFQJ8VI0Z/EFviHgCvxshIaQxqpSkl8sDNt8sFZ54t0prU0i8haSWwslfq6xuMwB0dHdLc2BTeHCNGiRCTuAck9F+dErgxVS8tr78jrz38uLz/zPOy4KFH1ASL1Cpx62prjew1NUrmujrpCDrCm2PEKBFiEvcIpWdbrfrVTfLSY09K8OFCmVDXKDdcfbUEbW3KY2juSaj76lJD7hgxSomYxD1CKdowUtIft8gLT86XupUrZYS6zC++8LzMf2q+EbaD+nAmGdNYYcxyXL+NUULEJO4Dnl2wQP5x3z0yojYh07afIu9++J7cfudfZfmKFZJMttk11I+tjmymODbHMUqHmMQKGuhTqVRWsoCL+vOGa6+T5a3LpbGpTjbZdGPZafp0uee+++XNN98SNcTSlmy1iwOrD/dAYLfS+SRGjH4iJrEikUhIbW1tViB1Mpk0cr31ymty3733yJQdt5NEQ42kgpQcfPihsmL1Kj1+n9TU6D11dfoUSExXU/jM7oCtzpXYbscYCGIS54F3nbe1tsrsy+ZIurFWpu2+izSOGyltibRM3nEH2WnnneXaa6+VVr2GOjG3pPVPTMgYpUZMYgWkpY/X3Wn6fLHICxY8J1fNnSvTd91Fttx6K2keOVJGjh0lY9ceL9N2niYtS1vkphtv0rqwutFqUuk7DtIZGvfiJvvpXgx3jBi9IiZxBk5cBKxevVquvvpqO77/V/aX0aPGKMHbJVCyBx0p2XOPvWTLLSbJRRdeKC1LlkqN+tE1CbXITuI+ICZyjGIgJnEeYJWff/55eezRR2XGXp+XPXffU2qSKalrT0utSvvyVbLRhA1l78/vLR9/vFCuueYaqatrUDKSnGqNlcdYd3fLY8QYTMQkzgNIfP/998uHH34ohx9+uB0bpZYYUlJPbhg92rqTZszYRy30KLnzzrvk/fff16sSUldLI1f3iC1vjGIjJrGC1mkE15ntW2+9Jffcc49st/32suc+e4uMbJJV6kKnavWaEQ2iTJXaxgb5xCc2lBNPOkleffU1uddaqmusoSsKmrr8H4hd6BjFRkziCLDAkPif//ynvPfee3LooYdIQomZhTIv6iDXN9RbfXnCBhvK3XffrZb7I3Wr67OudOxOxygFYhIrnGw0akHkyy+/XLbbbjuZPn26HdcL7BrrQuJaFSY/1KtFnjBhghyiZH/yyfnyzDPP2oymGDFKiZjECnen29vb5frrr5d3331X9tprL5mw4YZ+hQqzlbguPBKSGc+6RnadvouMX2u81Y3T6cCe1SdQdoTlR4wY/UZMYgV9w9RlP/jgA5kzZ45sscUWsueee4b11hr9q1aXkVnUeRGOQVQWBOjQe7n+K1/5ijWGPfLII/bMghATOcYAEJNYgRsNOanX0rW0zz77mJtshDWGpc3yhp60m0+1uGqFa9Wlbm5ulN12203Gjx8vs2f/Ts/FiFE6DEsSY3kZGx0SM3R/Fy9eLLfccouMGjVKvv71r0tdXZ20p9qVq+kMZ9UiQ2Ie4EQOWW3dTVO23UYmTdpSHn30EWsYa2O+sV0XI8bgYtiR2CY2KOrr620LIOFjjz0mL7zwghx33HGy3nrrWQNXuiMzRUGJDB+jDVtGYhX+UQVubm6WI444XJ+Vkr/85S99rxfHiDFADDsSY2EhYjj3N8TChQvl5ptvlnXWWUeOOeYYO9bQ0KBErwtTqFYkofXgsE6s5AxHZioyRLbZS4FMmzZVdt55mtWL582bl3HH4TzXxYgxOBhWJIZMEAsrST2YLW4vFvipp56SfffdVzbccEOzwjaGGmsKaVnJMqH1ZttqkiFhs1cI3aVQ4J5vf/tEWb58uQ0WaWlpsdO8Fxc+WnDEiFEsDCsSQ1rIhDV2NDU1yVVXXSWjR4+WL3/5y3YMMtLdZIB4KnQdmXSoVTU3u9O6usUFWOPdd9/NWqrffvttO8Z7Y2scY7AwrEgcBWRGXn75Zbnrrrtkjz32kE996lN2rCtClzkvMNIQlL5htdi0VFNvPvLIb5iL/te//tWsLySnDs61MWIUG8OKxFhDrLATi77h8847z7qGdt11V1lrrbWy58O6s1pcUigjCWlSK9ysO1jyTkLCTa0S6xG9SAk9efI2VijceuutsmjRIntvXkvMI1xixOgnhhWJ3RJCYIhKPRi3d/LkybLTTjsZ0bDEnGc/azlJJXbTIyRoH6E7GXc8c57r+Ecrdp1a4/Hj17Z+Y7qt7rjjDqtj457nJXKMGAPEsCJxFBD1uuuus0aomTNnmhX2CRBd0dWdXoOGdn3mnsxJ6tQ777yzuefnn3++TVNsbGy0d8aIUWwMO61ya/jQQw/J/PnzZZtttpGpU6dmLS8EXNNihr+zBLef+scvyyE+bvjEiRPloIMOkjfeeMOsMZaYQiJGjGJjWJEYVxkyrVy50oZY0gV02mmnZVurIal3A7GfpbLuw9NwCR7dgeRa97WtSwQMEqEwoF48bdo0W/nj1VdftWfGiFFsDCsSYwkZxEHXzwMPPCA77rijNWjlWkjcXshuAzsAG4isx7sQ0Y53Fejs133yk5+Ugw8+2OYm01JNn3SMGMVG1ZM46hpTL+U3AzGYbsgYacgW7TcGTvaOLsMuwxZme549kwGXIWmjAsyK6zX0QX/ta1+TtddeW/7+97/bcj9RdHlmjBj9RNWTGPcYknj/L6tYMmd47733lh122MHIynmI5+L1Yib+Z2Es7RvZoDf3824IfNhhh9mosH/96192jDDEiFEsDAt3GkJ5t9LcuXPl448/tvnC6667rh2DuP1BgPucK3aik+w8nwJjyy23tNbwVatW2WQJQLhcYsToL6qexBDUu44YRTVr1ixZf/31ZZdddsmedxKx31dCc0c+8XpxFHQ10cj16KOPyrPPPmvEjokbo1gYFiQGkOb222+3Ri0m/X/iE58wcqfUzeZclLxOZgTXWC+wa1z4bUILNUMudd9GbKlwOS3Yfj8NZFjeL3zhC7Zl/S6sMecc0f0YMQpFVZPYXWXquFhh5vlOmjRJvvWtb2XrvQMhEHfa3RA4+jvz10GrNO9l3S7GadM/HSNGsVDVJDarqYCo9913n7VIH3XUUdk6KZbYx0oPFnziAy3jdDfRYv3HP/5Rli1blrkiRoyBoSpJDHlxk93K0pCFBRwxYoR90cFbpNni7mKV+wS32mxN2M9IN6BBjfcQlm233Va++MUvypNPPmkCCAdhYOsSI0YhqEoSY2EhplvYV155xSY7fOMb35AxY8YYaSAVhMntI+4JxtcMkUPudv7rDryDeyDzyJEjrRDBvabfeMmSJXY8ulRQjBiFouobtsCf//xns4bUSdnmm9tbKgvI7CZaxu+99177XAzhGEx3Pkb1oypJjHXDnQbPPfec3Hnnnbb0zqabbpolq5OY336sUCKH1rir9ARvaPvmN79pc5kZOUZLdZ/d+Rgx8qAqSQxZIDJu69lnn22T/j//+c+bO4v7jDsNuGZAFplLc6QnInt31tZbby1TpkyRm266yerrMWIMBFXrTkMYGo9Yivazn/2siRPUXVh+sw+Z+4NAGbuGZM7lgzdwjR07Vvbff3/56KOPbIZTjBgDQcWTGCK6ODGxthCGrhwauWjQYlF4r3tCWvY55/eWArxzxYoV9j5mUDGXmcEfbo1LFY4YpQB5mSuDg4oksRMvKk5gtrjRPumfRqTtt9/eCAt5uQZrSD3U66L8jspggXfTR00YWRr3S1/6koUVInuhMpjvj1Eq5COwS/FRNe60k5Qt1u62224zYvznf/5ndnBHLkEGQlrLEtznXAlP5wXvSqmb7y3kX/3qV2WTTTaxhje6wTz8MWIUgqohsVtYiIt7yveQsMCf+9znzOL2l6wFo4fXEEYI7A1rfHGCOc3//ve/jcicj1uqYxSKiiRxlJDso/wMa4QcWLq//e1v1oWDpfP6L8J1xQIh8EkPudITCIMP9SS8//Ef/2GL9D344IM2OYPwIx7eqMSoFJh2dCPFR1VY4qj1oo5544032jK0rDiJ8kfrwkOJ6PsJE4JbzYQMPqn6+OOPWzg9PhA5xtDCC9DCRAtgPoebKzkrxPQkhaBq3GmA8vNJFiY6MEaZrhwSxElcToCghAtrTFhZj4t+Yxbxc/KWY7hdycJwqbBV5dTKfI6kqkISfYxLIlfUm1pD8l2n0uUZmesKQUIzo7y0pA+IBpl9lB4rR4MWgzo22GADueCCC2SjjTay427ZIEVhoARdKQkl2rIF/5Z/nH+ZfHqTT8mk02aKjGiUwD6stiYSicLqtbj+55xzjvzpT3+ycDO6zBGN61B7El3CEmi9PqHK9tFidX90v7FBJKkKT9zrldRWt7Arw22XoOdRuSGJWx/e2YUeup8n6OHBvCcUetzrWLR8rvFO1SHTI02z5UmRVZqma48QWX/j8HQfUBUkRrmRX//613LRRRfJSSedJCeffPIakxv8ur6jNCQmDk8//bSFm1VA5syZY1MWCWs0roWFvfjoEpZUq7z+7BPyxKVXydJ/vyltzXUavkZZvbJNEnUpTZvQm+gMc/jbYErdVe1KHzfepxINRr4gaJz5x4VhubRm2EH3oc95gRE5ioR0qB4tkZRsVDtKPtlWJ9vst5tMPOn7mfO9o6JJ7Fss7AcffCDHHnusfW2BOjErd9ASHK1XoiiFKUtpSAwYQ33GGWfYCK5LLrnERnSBLsQpAxJn07y9TT5+Zr48fO5saU62S+OkjaVjVSD1qVppGtUk6QxRs/e4NeqGBLaed8mRm38eNg8L9A3rsoQ/JDGIFEgZJJSc/FsT0WO6n4fEKQ3G8kaR5o9WyOonXpKpB+wt4/73h5nzvaMiSQy8PxVXmcYsZir95je/sckF3/ve9+xcrvtcbHc6dIPyoB8kBqzBRfhpkMOjYP5zlLhlReJkqyx86kn5x6zZsvVnNpctvn24HmzSJKtXwa22y3QfhXdygMz+Grpc6rjp+9YglCOSrx5sEN3PInPQntXTxfzmmnzv1HOJdgnmvyhP//5a2WynyTL6J/+dOdc7KprEEBhLy3rOWDGWhL3hhhus/5XzWOJo9AonQWlJjDX+4Q9/aHFgFBcNXuVGYkci2SaLn3hM/nbuxbLDtO1l85MO1XrxSD3RZB5KOpM2dg+SscwhovshEt2l5aAi3zv1mBEyFIty5HfoUETzQS20/g2P659wJwPfZ4v4c7oiEVDoaX34kQXy3G/+KJtvO0kazzg1c7Z3DEXKFQUQGAXBurKm8yOPPCJHH3209bly3BuzBhOeNbnSH1Do0Nd93HHHWV2eL0bwsbcooiQacmhYGjpQYCytCo4RwdOCJlGr9fma5lBqVeoy27yi3gaiVjx7z5BKYyRsGqY6lfoGk5rMNsF89Kz4MUTv5Xq7B9FnmGj8kDpEf+eINCDqwTTVSU1DrTQUqLtlT2IUNyoO38eVpltpvfXWy47OAk7ySgDhxKNgu8UWW9ggFQolCieOYYHdCvPbpdTo4gno+2tqE1JXXyPtuMyq/FhhNccqdUrumozUqvAbUaXPiiq9Sk1GpMu5Ugjv93ARxqh0DT0rmtpR4qwhTSXbtQ4fkgexVOFPRixn2M9kUVKv54D99Jv8RpMaCdIprYWkJNmRlNZ0qx7sO3hUWSNXaX0fy4XiL1iwwOqSrOvMOGRQCitcTEAOPArihRVmKCbdTnz0LZVKZev/XBdNi6FAtkBRzUlrMrer8mGhpG6kpGtGqOcJkaEBVjpUemsQUpe0U5QegdJCRXQfie73WdIFSpf7YVuuEEMasLRQwsVF9HeKL3ak2uX9t96SuVdcKbMvukg9D72GwstEb9SNy+qVK3mQLFmyWK6/7jo5+6dnScvSpXpE845rPPv0lSZs0pou+py0/kvVqGtdADQ2lQlaMyHxWWedZZP+Z8yYYe5oMpnsajEGCeRDXj1Q6Q+80Y2ws2gAX6iglZ05xxRKeBzErbxAKqSNrBoBAm9KGS1keixwLBEHIIWiL8/QY10uSWs1p7lJligJZ8+ZIz8+6ydy9z1/QwHtvHJPOrSUCoV9kRGjR8qixYvkL9dfJ7889xy5/Mor9NgouydMn06xhwDTWcQP9B0VS2IizTK0uJ18IoW5uSg7RAZFtVZFfFRPgMiQmMX8dt99dyPu7Nmz7RzxIn5eQA2VNea99m7bhlUA+63hImgeKj2a2esBrrdDKb0grXFr08JzzFrj5PiZM2X7nXaUj5WggUY2raR04qb1d7iPNRW9fi059OuHy5QdtpPW9nap9zELeg1teJZkmd8GLf3T1pWl//uQdFGUPYlRWpcosErXXnutNWSxgiTTDVGmwruReoa+2f46LH0zP0M3cU3pL4ijh59FA/jg280332zDSIkv8ctNh1LCCWukVWCDSRDqivrXjpEABDFMtzBO+YVz5SL5wqcnCH9tjdQ1NaoHrsfqaqQ12SbNI0eK1mDNG0yqy53SROA3VjmplltzStr1d+OoEVKPUalNyGqtdjCYsh3XW9GhXqTthj87Yemb2e8jKs4So0AprSfOmzdPnnnmGZk+fbp9Y5jj1B1dwSoRUeXZeOON7XMz1I1ZocRX6KQK4Y1gQwp9v4chGpLKTf1OEAeTMCuyqFVrWlOn3p6613Q+Llm1XN544w0rYGvVvNISY3qoxObeDrWsq9taZdXqVrW+CUl1pGTposXywYcfWSHHtVkiZ97l+V8IKoLEriyuxJCYqXuLFy+W73znO9n+YM4xocCvLzoYSpgIG5kGE8SPeBx44IHW533rrbfKyy+/bFbalKQsCiuUTcWVjvBYmNYMF/lSafBYRGOT0nRfuXKVpT1zwA897DA5+Ktf1arPbnLn3Xeple2QtF5Tn6iza8gvqkC1SvxFqqsXX3SRHLj//nL4YYfL3LlXyVKtZ3Md9W5NJEsnS6uMte4rKsaddsWm9ZZlaOlHpTFrq622yl6DtcodL10UaJqiqkFCHaWaVv2hiW76G743V/qD6P3EgbgwC+v00083d5pFAyAvs5y8fjwUyMYR0USgI8Y0PYUTaQ52F7S1JdcgMXX9oQOBzSeA0IedS+E/OpagCHGukeamJhk7Zoy8/uprcsO118tB+x8gBx94kCxf0iKnn3qqPKqGpVnzrV1d7jo1xY01dZLS+C9buEju+/s9su3kKfLzn/9M869BfvGLn8mHH36gRNen16rO6k6dbtMpVqgpLG8rwhKjBJRYbCEzK1gyuumQQw7pMj7alGuQED6Z9yCa6YP3qi6goGKa4j/+8Q957bXXZPTo0UNMglx4QnS611FQ4HDcu8k8D5GhQZS4UcmPsJ1DSaxC1rer67zu2uvIQQccICfOPEH+65QfyHnnnisff/ih3KUF7aoVK6RRiVyvRKQIqNX71x6/tuy2y66yw3bbyZaTtpQpUybb8snt7UlLh7bWldFkLFiPK4LEXvpjod555x0blkhd+NOf/rQdH1yrVCK2dgPi9+1vf9vW4KIlnkz3Qq0ckNU3Cw5/wnAppe0foM5I+K+//noriFBgcyMjUq4g/WnAQjo07TvaUzJ+rbVk4sabSLK1VcaMHCWf33Mv+eSGn5CXX3xJli1tCQeI0I+sUq/WdbRes8knNzIrzqAkpshSEPMZHy/coii0cbTsSewZDFGpY1x55ZVWl2Bwx4QJEywRcLO9nuiEzyeFQ++x1/u282epgKfB52eYleVDMUkLlKDUyt8lLeknSWie6BYHVA/acUJkfhGWC1HgipJvV199tSxatMiOEXYvjHKlXOFhw5jgYZA3VHvoEvzMZz5j570XwerCKpznN54jBTB6yjF0mEZLrgmrgDzb416YglWUJWa64f/93//JxIkT7ZtGRN4TCoKjFKZgRUWnMg4FKKCoG7O8LUvwMkKNOHp/+JAhb5JkFJH/GQHtar2ee+55Of74422GVtT6ODG8z9luLiMQJhf/vXr1avs0LXkDEdmimzRCQmh0EcJCaNowvC3HSY/QJUo+ci0yEFQEiR2MYGppaZH99tvP1m32hAUkiNeNqwkoAAvf43lgjS+88EKzZsUvrPoD0lvFFgBg6yTsSsR3331HDjnkazYKjTxDsaN55/ckurm/eOj7cwmfewpsKXjcSEQJyeIN6CSuMQOOxo0blyWvX8s1GBvuR8hTfkNerknkkLjQnC17Eruy0qQPiRliyQQBwDkSGWGfhKk2oAAo0Oabb24L4fOJ1meffbZL3PNJSbCGtvl79UTGnW5PpmSDDSbIZzbfQq1Th8WlqalRlbszrzy8Fnb9F5KHgsF+2X72t17DMxCsXXitFiGMO1bx+IcS3tMJApxf3BNwicKIltFDSMmSyHRvch1kveyyy8ydZlkliHnaaafJxRdfbNbarSzTZYETHF31LqZkcmANlWVPYkotMop1pCHyzJkzjchE3hPWQcLkZkAlw+OIQOaDDz7Y3DCW74nWLaPiiO4PDnp6fic5zGrVN2h9+Bp59dVXVakTZsU67w+3/LUw20/ikiGuxSvchwDoglsxhN+pFDrSNR3s3uw7ougMW1Ts1Zl7HaS7v4d3rr/++qZ/uM2svPL9739fTjnlFIsPH+5jaSXaLFidhfr/7373O2vQY+03Fq3gQ/eMwKNtA/f7lltusTnwDQ0DrBppoMsamknBG2+8ERx66KHB1KlTAy3dAiV2oCWxncsnfQPX+bVsOzLbKPR3emUQrF4aLH/iieCWY44JFvz4jCBYtUTPJPU89+ST4iAaJ+ILVGmCrbfeOlBlsGO5Er1nUNG2Klgy7/7gukO/Grz0i7OCYMWHQUd6eZAK2nSr4U1pSqisWtUazJ17TfCZz2wZ/O53cwK1nkFLy5KgtXWV5mNbkOpo12NJDTt5mtmm24NWff6yZUuDZLI1c67dXksctR5qz2EfXVBy67ZDj0XTIqVpoAHoki/dp0nnfd2nof/mfW+++WawYMGCQC2yHeOcWljb59iqVatsn+dpHdrCiajbbdf5e9gGGt+gY2mQfvC+4LEDDgtW/0TTswBUhDtNaYULydI1vmSNuymFQUvazF6I7kprB+dUIm3+lNv2t6fbigTiqXmU3SIsNo8b+fe//91aPLsD95QGmTQyaFj1r3XJqLdMA3aqPSW//e1vrSHu/vvvt1lZ1CXr6uv0anWB1S2uyXhQrE1mK3yoG15XWy+jR4/JxlsppRL2QISWXC+ze8JqlBIieyxEcePP8/3ZvI9uIibe0G+vRLTjeEnsM54fz8kbvdhnyzNo+EKHuY6ws7WwZ9sD0K3Cwl72JEZRaZGmO4nlaIkw3SsocqEIs8AzGUT3u4EnbjRdNZH5Vwp0KqVYhk+aNEn23ntveeKJJ0xIj9wCrTQE5h0uXQE5CXZHR9q+xuHjwB+Z94i1rkPiWmU5I5QsfirLl6/UuuZCaWlZJgsXLtI8TqripzRutXpumbzz9juySI9zPUIciTdEeeedd+XVjNvq5/IlQRiu/OJuMxLeH4rdp+dJZ8QJa8RTUF3gmD+He9gCCi7vRYDgXOt55c8mLSjECF2YlPzJE/geUFYk9oSIggn/TI6nPkjXEiAxcq/rC/TpmYzkXblWmH2X8oFntisV8eYjcRRuTMWkhB9KkI5hXjCum9RTRdZ/qfYOaU+2y/U3XC8nnnii1SFRZOqD4bBCyFIrrW2tMuf3v7fGSuqSrL2t1SZbcpj6JfX/X/96lsyaNUuOOuooW0CQhiHAFzMYCHPZZZfaMw466CB7fne6AfEo/HsTSJm1kBF4HjjY5zosc18AgemeojUbHS4WytISe+LRkHHeeefZih3bbrttNuK4UwNJBMtiMpqV9ls+Elndogd4Z+iyYeM7UEhTBs00/R+qhWZWwHsLKymLBVcuFsenpZqGERpISC/CikSVbNAR8C7eq2lnr1W3WFWKaXb1DbXyyKOPyLrrris7T5tmYd5m8jZy/fXXybvvvavX0tWSlJdffkW0qmqfsWE4LZbpK1/5iik8s7fIZxqQfvGLX8iXvrSvnH/+b+Tqa66W9957z9YZZwTUj3/8YznrrDPtA3p0wZFGnQgLPsj59ltvW7Usn9Do5gLR8Paw8q6LhMfTGHg65xI9F369g4KMfv/e7isEQ05iT5jcyBJJn/RPH+lOO+2UbZWMJmQ+yQe/h79p3WcplNSiRXLHeWfJWw/crsQl49Oyun2laNZJkjqYJzTPVKkJmlT4TGrpks3jw9b7JqlaYHVQVkZCkSaENTcNBxeEC4Jk0lbDl6CAC+qVnB3qKbTadNF9Z+xrdeMttthcXeov2P4lF19s1hSLPGXytvK1r33NPArqi0cccYTM+vV58t//fboRe/31N5A333xLnv8X++vL2HFjZPbsS9T1/ii7rhqghXrdddeR119/3QhL2AhH2lqtE3r9Imsh/71a7HzCcsd8fYM1vyk4IBt1V9LWx6oTT9KZvOB4X+D3eP4gXhgjFBgDxZAvWRt9fXSfPjRK4IcfftgU9bOf/awlbpSk3RE2H3i2JmXmR43UqpVvfeNVmX3C0TLj4ENk0pHHayUGS6vkbhwtac2khF5fX6fuqirY8udetyVrP8WStT+cqUWq1nXQyLwoPskJfzS+WGCWt6WOSbcFA0E4j7L01b0bEJJtsvTJx+Wuc38lk3fYTrY65fvS0TBK0ol6W0judbVouMK777G7TGTts0Qgr7zyspx77jk2r/b22+7QMH/SrB1uM4U0rjF5TkH19NPPyGmnnSqHHnqobLbZpyWpVpsFqhj5NWLkCDni60da/Zlx2LinfFSebsjbb7/dxmejK6QDhKbwo5BAuvPgIJPVTzXfuZ609PSkXv/mm2/a8bCACC1zd+kdzaeoTjuRfR9QMO2yy1RZZ+1GCeY9LU/8co6m52RpOuNHdr4vKL62FQEkEI02TDlk7WWG6pHA0cTpHzQBPVFTaWlIdsi6iSYZ0dImL97zsDw85wr5eN5jUteeknpNZCZ15yIMAX8HGpbCkBt3rNCXv/xlqxtT5XClogoSVZzBRPgerEtnOnGIoD740IOybFmLTaOEBPfee68sXLjQWnUZBMHUSiwcLbdYYEY8hT0P6mnp4yAoDVmQm/yfsc8M1YV95Lvf/a4cfdTRMm7cWkYorCgrvGCRsZ4UCOiKk8QtJukCgTmXTwiHb/0ex6abbmrVF4QFKAgPRsWPMRnH93uSaVqt4D7uZ/klhg6zuukoLYi6ojDdKpvF46PBwNX6yU9+Yo0UNHYwnK0YUEfGlCwd1EodLtLrr8qNJ86UUU1jZek6m0nT6kXy8YrFcuSvfi5NW24hyfoaqa9JSkJdteWRxeO3PO0EkRENobbmxeCXjaQXZMBSMYLoL3/5iw024HiuxzIoaGuVxU88Ln+b9SuZsuMOMuk735VgxFhpSyWkbfVKOedXv5TDDj1Mttp6a7OADayrrDlw/wP3yZFHHKkKvbMS8A9WGGGN11lnPTnzzDPtM6+NDU3mgX3nuyfL2WefZYVVaEmTSrQGIySW8wc/+IE1drKFwKxH9stf/tJW2wBRq0sa0YaA5xJFbjrh4vJxOwhNQcB5JzXn3LJzrDvqRJ+Zew2/eS7CO0DCWmGWqyV+Ri3x79UST1FL3PcvQJSdJSaSJLTVp/bd17pUilFvAPQWqZMU/qjVqNclpLahTsZuuJ4c+qNTZL+DD9A6b1JeefEZZXq7Jk726rIEVgMXFIvGkFQUHcXoTrmKC5Q7nKlTR1rqb7qUINg8JSB5NnHTiXoNKRiGBxJgkaZOm5qdWskxMGKEr5GWUFKvllGjRtrIqCsuv8JISRx531tvvWVfx2B+Na3TjMfGknMvRIVkEIQtx/z5EA+rR/tKVLCICBafsHEM8AyIGiUrcXVXu/jwPCv82WVHYhKf+g3WmEn/JCB9bZ4pA0JA40smkTST2oMO+Xi51qs22VDk0+tJ7cT1pCW1SpatXKL+1yrlcVj/KUegSBCWPuPNNtvM3FVcV5QPkFYDTq+eoO+vVQVnDLTVCdUN7kh1WJfRhRddaF4B1tFJRLgIT31dvRx4wIE2bJT5xQz+oH+X5ySTrZbPlLZY2Kk7TZV/PvigfVuLDwTQ6PSrX/3KyL322msbsdGVF1980YY0MiwX0mHF+cok7/Y0oO6My02DYFTo2kJYbBF945iTlGex778pJCmkiAv7/cFgFABlQWISmwwhwWmkoGuB0hHlREG8RBxIAlhmQuC0WhD0PKWu8vK0jB69vtQ3jdMc0oPJQMaNGiejWAydutlgkmCAQJFIN6wxLigKzLpjuYUd+y5FBe9XIRzUQ/VN8tTTT8lxxx4n99xzr40ou+2228xVxnpR4EBw6sJ3/PUODWe7PKCu9Te/+f/kxBPxJlrluuuukyuuuNzGWo8ZO1r+69Qf2EL6Dz88T3529s/k0ksvUyLuLvvvf4Bsv/0OVpW49NJL5cgjj7Q6NXVM6tVXXHGFeXDeuBVacS1kMgVKFJ42nAfoGPfxOzfdOI5B4Rz7pDXCPVzH1nU0dP9DorP16wBhIj2y12eO9xv68iGHJq6NhwVnn312sOWWWwZax7PfxYIqWxC0qyR1n2HPy/TPUy8Esz63V/DoL84NgpYVQfs/Hgxm7fvFYN7lF+r5j4NUBxcu1/sWB8vmPxnc9s0Tgxf+99dBsGKVPiR3XG5USgO1CrZVFzM4+OCDTdSltPR0Id4uRYXm1+IH/xlc/dX9ggVnnh4Eq1rCw5rGrW1tNrbZ38k++at12mDFymXBhx++HyxduljPh+ObfVw0YMxzqr1TQEvLskALqGDRosX6rHSwcKHeq8msLnugBUjw3nvv2bt4x8KFCwMlrb1TyWNiv3XrYRqIONjnuQ7CET3v4Bjvjb57TWj80wuD9EP3Bo8dcGSw+sc/zxzvG8rCElOyUcJR37npppus7kJLXr6SszjQ0rUhIem1R8lWB8yQxk9tpMWjlqxrjZUt9t5LNpg8mTFzksSqZe4oN2jemRUEuJcMSaU1n7aE4oIUyJcKekwtCHln4cB1TTN6CUtWb9bGw8g++Yv1YqjluLXGydix48wAYZGx0CCVSqp11zy3oa4hmL6It4E+jB+/lr2W+dVqI7OW0Vd44T242Vg53F7er+Sx6/Aa3BIWCzzPddSXHKLr78knn7TVSX0YKOHy9Ch2GEDZ1IlJbF++hSF6tFoWC5p2+scTr0M9anVz6lJSs8E4mfGt42XbGV9ksJE0bTpR9pt5gkzcbkc93yCNqozWtGX3upQPcFNx1djSwEM9lC4XunIgV/EUxhIwIxnoLlxjDHT26wYc003YmNVZp4TICApvx/Sf9dqbgtfJiGYlgA220Xs8zLqBqIzmalBSQn47rOcRrqutUbc38xlZnougR4A0AZDHz/m9A5EoeCaAnOQDdfwTTjjB+rpZSvmnP/2p9Vn7+dz7i4WyIDGRpHHinnvusRkgNC7k66/rL6xV2vRPlcKWm01JUv+11WhdvLlR2pubbXCHUBduHKHhqVfl0cy3e0h4F9NT3x1yQAqvWzGjhpZVRjk98MADVg8sjtJYjCPbDDKKyeqPdgolDw+vcamHg60TyqAXm+XVG0IrFR6OglUv7Jl6ji3XUGj4K3iWnc+A3+6hRC0g1riYJIrGhffRkEY3H8so0RBHvjCHmD58CpaqJzGRZIgl7jSD+3GJiHBRIh3J4ECZjAWgX07tg51irK86fCZ8XpNhg4mUin1Fz24re6Ck4Atf+IItmIAy+UoSxUEZJkQfgzRYxHE4mWnE+/nPfy7HHHOMeZJ/+MMfbLnhO+64w0Z74fZ74VJslJzEWA+PDFsUkMHstKwymoeZKpCa466cAwJ5mBUtGNT9SyQa1A1rkFqTsCUyoXU5vrejB0Jh3/s49T+WXGtYWhCo5UEy7t9QAitDWrmiMgGAGUDUybDI3h3SP5D23IuwHxE2iRqzNvX1zWoZGYJKS6ymCefywAvlcM4wBSaqp96Opr+e1X+4u+F84lDC6zVrOG2wDX9yhU32+V1lsOE6SvcVS/S4G89wSkgM3n77bcuHwQpPSUnsxIwSlGGDdNzzXSUI7G507rV+fb9A2mlMcc0SNWpla5q0PjVC6mtUAWtVEc3t0kxHnxAG0tTpTRESUy8OVFGDBF+AaFMpjz5kiOwKS7pRH6ObhX5TuutA/9KOe/BW/B8FbkbCC0Ko52KJZoVb2BAY1VUPWyih+2mFpv5jS/j1qsw56q+ddVjO2bX+PN2yn1863+P3R48NBjxd2UYHifCbLYUcfeWMa/fClHMuxULJSOwBd6UjUp7QTPpnuiEtrN7aF6Nn5ComaQnoWz/ggAOsesIUO44PLE1RtuIpXDXBicgWwgK8H6wxxgkLzJctaT0PC6vBQclI7MRl6wqIcuH2sYIjQywpsag7lBXUAmvow/0IgjzHSgkvFKMgfVEiPBrAcjgoE0R2S9A/RN+j8bafmo+6NbHjIYY2VUqLaEFKw1WUzKyGySSeo48+OruET25+rYFeTneHkrrTbi0ACUALKpO9+dYQM0E8kk52tvmUtXQgkzTMdKdblzpdI358aOFp4ulD3RhQ4vN5G4ZjYo2xBhwrThoS70zc9XH+y1r+M2L7wwhOZNLYPR4KTgpQegxoo0CPe7XEA0i3kpKYCLsysc+4VyY7MMRyypQpdpzzTmISha0n1JDAE9c1NaulQxgmhVdFSCsnsIN2BVpIKSSpqoRjk/u3pFGM7kH6k6bkhZOU33iXLE5ASzWreKypxxld6iL9R0lJHAURY0A7EWMAOo0xJAS/3f1zxRt65StOYhcTpA9CWuHCuZIgkJrpm4wfZhwxZOaYWwoQTdPBSN9oig1EyhWeZm5wAPrLmnAshnDSSSd1WR+9czZXPglhT+n82WeU3BKjUNQfGAjPaBaa4ZkoHUWUzGw9kWJ0wtPF08jTzPcZisnAAwrCs846y7YIdWYAoVFA8gOgbC4hSPPC0527vWOqGNKTTnOuFNIdSEPSy9MSr5LZZFQRITDtO+QHM7VwsXma/szm0xrQl/VH00tKYiKKq0eE6BdGAWmE4XjZIpuqYZZ6rXiokU8R/JiPDmIyPa3+WAdGxAEInpvencTNBc93KQzROwcqQ4nu3k/6egFKetI4e/7551sjFssEMYuLWVksLcXXISA63WghQl3qKiH6E9+SW2Ii89JLL9kQS/rWvC5cvvBkjSS4/h9q5eoJKBfEZLL8sccea+PRmViC1YXEuNbkRffkjYKYRmPbc8z96mKJIZL0Ucl3fbGlO5B2kBdhssPpp59uo7b4dAvjpk899VT5n//5HznjjDNkwoQNNC/GZu505ETG86Knl3aDkpOYSLtCMQ8UFw/FioLr8snQIMxODblufKCDJlswVOHpRHdp4m0JgInuTCahtZTVNDjOeUd0H3SbzhZflYyu2X4U3Gf5FJ4plkT1fMglAtIJvSX9mHjCR9VYcpdqIg22t956q+2zvthJJ51s9zBgBv23gTOZf1mkw/0w/S3mfUZJSQxotXMrTFdIVOHKEzkJaq3ThSd0KeHpicJQB2a9MhYNYMULrDCW2hElbbcEzoucaymImVVU7DENvIbg5hPOlVJyQHohjMpiyDBVF752QaHJAA8W2EPH+dwpNXxMASPSlP7s2e8sshzI86JeQFIMClCkXHLiSjNdC7BAOBMdUKryJnEOCGoFBNeJirVg4X2qLVgHlgIGhRFWke1iC3+uARrM2tukPalWJqVeS3tHcSTZg+S7vsgSpDqF70ahwwh6a7O4MsJvF293YJ0xzq1YuUJa1fNkxlZ7KqnXIHpfRjpUHIVTmKwpIoPyPYpjCBGj7nDYYYdZ1weLdfN1AI80Un7Q+ASawG1JWfn8S3LvxRfIphM3km3+6xSRZpYZjbiiXUgxaGVjn4ACeb2Y9MUaM7OJLyXw1QQWa4fEXOdkDrdh/nXu4/BFGsECjmeub10pi56YJ09ccLmsHdTIp3fbSVqbR0irWhpyMnOV/R0IKDvyPSV0RtfUtxDdv7eL9esGFs0IurylD1Hq5EHY7tCBjttaZLkj58LQaE7JCJW2t96Tt59YINvtvKM0/O/p4SV9wKCTGIVAkRCUiGVDWZqUbytxPYLCRV288oHGpzsSN0VITE5kyBCifOICgUljuvNYGZPRcXwA21eIdESJ68Rm34gSzVazyEr+1uXywVOPyfNzrpO2F96QUfV10tZcI6vqtN6XXWAwmiZFBrrTJWBR6HvznLJ4DWKQCgNhzBQpHYHUJ5XsGqeOuhqZuvvn5BM//Yld1RcMGol9n5KHfeZU8mlSLC5zLH05E0e5kjiQdklA4ucqk8QsVOeFpH+mhHWVmSTRSVaC7/uQmPCHeZNfPehqU6KuWiqrnn9NapeukAZVvmSN1sFVapiSyOdT7NJ89xcH3T+6mxMax2gulQMoE+sSdVIXYIs1VZUvTRtuILLVlpkresegk5j6Awp07rnn2ndqmTjN8qCcjypR+ZI4ZSRe9dwLcg8k3nRj2eYHP8iQOFMFIBplSmLvMwb0ZR5//PHW+MLXBbHK5ENu2kfzpVv10PpdArJidc1FDFvv3VJ3S6TuEE2+bhG5CJ+3yyv8HAczYmGJQq/p03siyH1EX9DXd1gw9Q8LUHQ06X6m8FSvRkb0fSJQUbWNzHcF8H3caBb/ZgE3WusY08uxbpWjrKBxQVnY0/D6P/6XO0hfxIdkQtStt97aRnEx+IMZNhzHM+opLzwfkU7ovlqPQBol2aT14BEjJNXcLCnd72hslqAfwrJIfZIGLTyRRvXksjIqI9FjatlyJO/zepX84e1J8j8nj2h6mTFAmnVfJWgeKen6wmbyDbrJYIQWE/4RBh6gVD5dK7+ClBcyHF4TlVAGKajOQFRIzPh0psZRmPKJHBabp0ANhwQCIuVWlK1aWttm9s3SdmiaaD0702fOQkfYZIjNP1OpQD2UzBcSiyMNKqrYtvXffkwljehv22LR9JrMUkvlK5E4abUsnChH+tIVVZhyDTqJGS3EIHyWoWVxb1+hsZyJW02gTuxdIlhcpseRDwxMoGAlH+jn7BuyvoiSOGAdfkO4QZVCCbSaEaCYVt3oq9C+0J3oeSsYotfzrrDwWBMeluj1hIltvud3L8Qj9zl9kzWf1VX0Go1PmFYqGg1bAy4jhYCYFh0ohjelz58/X1544QXrF95www3tGJYY6+BWOCZ08eHp6rPDGFTDb4jMFyP4zfhe+jLd9Q4J4eTQrREH7dKfeowBCqGC1uuhGq3Kqbuuew2cozGMtbNws2sQVUzEjvVFuL8H8TXPTMLg2XKkSG2OcE1/3tGt5HtWb5LvOTli4czECfi+nioEBV5eGOjeoD8Y8vKxKmZ1oCwxaYcOpD3989SNmYTCOHYQkjgH2WzSHatXQOTovxjlgKKTGGWAvNTB6Epi9gwrAeLGRQcXxCg9yBfcaqzzfvvtZ2723Llzex76avnVKU7eqMQYOAbCi6KTmMCgFKwmwaBwFIYuJbbl2Y00fBBtiWZ5VT7nycwbJka4u52rTFwd1tfC3xygykZOMvrXJfqvPyBc5Sj9Qb7ndCdRePrn5kFvGBRWETjWd8IK77PPPjJ58uQugc4NfIzSwNsh8Ij40gaLzTPohoXOsdCA2WXenkEuRaUL4iwsGwwKifm2MNOwaMDiiw4oBa2krhwxhg54QxSiuNIspkevAXVjZpdxDKJD6HTQmVcxgcsbg0JililhMAFuNG4b8EEHMYYeNDBCZhZxO+6444zAfBParTSudZphkxkik2tdci7ngP90ibrZfPjMXcRiC3EoVPI9pxxE/3SVAlBUEjNoALn77rtNGVgAzxPOtzGGFl6V8TxhDiyrjVLoMssMAnOcmTdYXBSEXMuXc9Hjvp8rMfoOcsalEBSNxCgHAzlY5xgS06XEGN0Y5QUICrxAZfz0N77xDfsAG4s1+NxY7w5EupAxws6YpOWBfpPYMxjxEUHUp6666ipZvny5fdGBj0HHKC84eX3LsNhdd91VNt98c7nxxhuNzH6O/OwNMZGHHgOyxNmSWjOdOi/u2A033GDfn9lxxx3NNYtRXnCCAvaxzP5NaD4ty5pQVIUomOlX7gtiIg8tiuJOowxY32uvvdbqxEz49y/9R5UmxtDD8yOaLxCZgpdGSL4YsXDhQiOydzvFKG8MyJ2O1q9o4WSEFm4ZI7SAW+kY5Q++pkiXE+PcqRvjWcWeVGkBU1wKQb9J7OR0t4tvDNOoxaRzFsCDwMCJHJO5vEGBvNdee9mXKVn0nK8WxHlWOjh5XQrBgNxpBnBAUobt3XzzzeaS8dWBGJUF8hBh0QC6BVnalnWq48E5lYF+k9jrS7hcjz/+uLlhJ554oh2rRgRaPPanlKwUQGJcaGY30dBF3bilpSW2xhWAfpOY7ge6J1jHmK4J1jamXkVfcTXCO+DD+dr6p8CJ2+WOcJRW2oZhHnHEEbYeF4VzbI3LH72S2F0tJB98ogMt0qyC3911Mcob0Xzz3gW6m+h1iFHeKMgSRzOahhBG9zDpf+LEiTJt2jQrzWnoqh4QX7VErC1lILn67bxUDPj0CEv4PPDAA7JkyZLM0a75HxfW5YN+kdiJSpfSv/71Lxt7S9cSrhfk9tbonqQywJBDPrGRCufTsqgZC7FVGZFz84Y1t2igpMp04YUX2qw0QP7TmBmjvNCrNpJxLm59yVyG5/FpEL4IR/8i9WOOV1/fYsQSh0sShvtVDIhM+wbWmG/tMhLPES+xVH4oSCOxtLRgsmXWC/Vhxkhvv/32dn44ZOxwUF36/VmHa8aMGdZwefXVV9tKLW6p45Fc5YWCSIwVBu+//74NCPAZMNEZL9UHaMsyrGxdqgued9E8pKBm5N306dPl9ttvt2oT1SjO43HFRC4fFERiz2RWSKT7gQ9YswAe5I4qQNVBowWJ/V8WVchpLC2FMkRlFtpRRx0ly5Yts/YPX2jPq1QxygO9kjjqIlPfxb266667LINZMRGQse5qRa+vdlBkuVQLKIi94ZJ8ZV441pjuJurGtIsgVVtgVyB6JTGZ5R3+lL58cZ5Fx6kL0y/MOUruGJWN3MLXScoqpXwSdfHixdbIReu0t4vEKA8U5E6T0X/+85+NzEwkp0WaY5TMwxoV7nw4gdki5G90O2XKFGu8vPfee+2zPLjXILbG5YE+udMuzz33nNx6662WoaxZjAXmeO51wwGBRjMr/I5ItYEF9fgMD/nPypj0I8d14vJBn9xpQKMGXQ1Y3T322MMGyUcJy3Uu1QXimBFnbeZ3lLgu1QbPU+rGFN6XXnqpTYyIUT7olcSQlvoPpTCTxVkInkXHo6TNlepBJ2E7idtJ4GpC1JOKincr8j0tPgRA4xYznKornysbfarM8uU8ZiqxbAvrFDPpPxXpJ4wztPrB7DRGcG211VZy5ZVX2oi9GOWBXkmMG/3OO+/YCC2G4jGKh/rQcKkTJTo0nh01UpPm+75acEWmIIZ2Od8wEK5xqWxgjR1MjGCiy2uvvWaNXF54x4X40CKhGdBjDmBx+Uj4rFmz5JRTTrGVH3Cvo90M1ZqJ9uGwZe0yriaQD158Uu773Z9k8y0myeYnHC3tI5olkSnI1PHUP5SHocL7lxPst9WhqwPkN4N8fvvb31qez5kzR9Zff31zudEHCM/xuNGrtOiVxFhhVuygLjRp0iRrqfQupWhfYTUSuUYJmFjZIWPqa6SjbaGstTxphH1zXLPIqJEZGwyoP3Y6NV3SosInTDgx2dIbQX8xn+mhcD/jjDPksMMOs/OQ2K8b9l2OJUavJMZt+tGPfmSZQ0YxYov+Ydxsn7HEI3p5TEUCwo5vHCttrSskXbtaRq5qk6a6BlkxZoQsXb1a0hZls8O6ccUNlT6LCrbExIN8d5DfnucU4EySuOCCC2wmG6O8nPCxJS4teiUxs1dolWayAwup0cCRzxJHM7tqgCUmihq19lp1GTu0TqxxDmpr9JSmAecjbnQnor8rM116UQtr7GSdcdpIcKkB+oBuxCQuLXr1eyh5qfO4JQaUuj6+tjoB8TLk0xTqUElLnSRr6yWp6ZGOuM754fdXJoH7CnQCtxrSQnoI3Bv5YxQfvZKY0hUikzlkGr/JOLfCHKtOK6yi0UqrhLsJ6ZBa6UhoWnCigt3kYgICRz2yGKVHnywxiJa2WGR+R8nrZK4O0fhoythWpVaFVMAPqVNG1+ivRIL4k3ydaeDI/8zKEvIZyXeuN4lRWvRKYjIl10UaTplFLBESqlaToZZ6cPbo8EiD7hDVAd8fLnpRTuiVxL1hOBEadMaV7YCTL0aMAaMgLcwl63Ardb3A6hSO4XJ2lWrCmnEOBeChucQYOhSscZ6Bvh3eIA3ySYwYpUPsD8aIUeHolcS4StEuJX5jhfntqx/6dDWui1F9II/b2toszxF+I7Rexxh69JoLfPmfUVp0KTHUErA8i3/DFuL64A8nsWcy0ldE7yknKRXyvbtcBB1gRRfWV/MBHT7wB53werJLjNKiVxJDTjKM/mIGwM+fP1++973vyZlnninvvvuunYPkEJgx1W6VY1QHICVWmEL78MMPz85gAugGOgHJYwwd+jR2msXDx4wZY+srXXPNNdmPi//pT3+ylT4A5GUZW66Pft60ryVzL8EYMpTKspRr/CmcGSd98skn2wLyhJMx9CeccIKtP37QQQfZ2OmRI0dm4xC72aVFrySGnKyrdPfdd9vCAGQqy5hynK8/bLzxxqbouNteR2br6AsJegnCkGK4k9jBah5vv/225T+fPUWYFINHhg4A4kB6xSQuLfpkiSEwVpYSee7cufLMM8+Yi4Ul3m677SzjcLedvBDa0VcSlKsSD3cSU11imVqWZeLD40w/5KsQfOLl4YcflgMPPDBbkHtaxSQuLXolMcS9+eabbUGAbbfd1hqzWDz+kksukfPOO8+WrqXFkozzFuyo4sck7hvKNf40XFGQf+tb37L1tSDzhAkTzBOjEIfEG2ywQebqEKVKsxgheiUxjRZ33nmnra/l9V/AcUjLGsQ+ScIRfWS1Zah3s0S9DdBdnCs9/sQVF5pvFLNMMeQl7ixbe8stt9gKmJC6mvO83NFvv8dbpXNdp17KhIoHVQbiXO3xdBBPSDt69GiLOwSF2D49dbikQzmjKCT2zKz2DMX6PProo/Lee+8NG2sDgRFIC3mjJAYxiYce/SYxmRlV5GomMi4kVoiGnVNPPdW+EEg8UWYXXE4KNB8QA6qJ6MSX+EBo4pqLaoprpSFuRuwFKC/kRElpB2DRdLY09tBqC2m5xt3LfApeySBOCCAdKLAY1EM8KdgQPx9jaBCTuAegnCgtyguoPqDA8+bNk9NOO01OOukkmT17thEapeZaBj2AarVMpAVxJX5RiTF06JXEuE+uzN6wwTYXnpHRjPVjlYponABuNUv2fvDBB9a1xhcRzjnnHHnooYfsGlfwaoLno6cBYB+dYOQeoBsyxtChT5bYMw0FxX30OqLDMzia0dUCiEnciZtb5b333luOPfZYmTlzpv2mH93TiEKvGtMBeBypOrDPyD328U5iDB16JTFKivKSaWQWv3073EAa0ELtLbVsmQDA6DXgnspwAPGH0N4mEGPo0CsTUVBKXDLN630ujuGQicQRwvJFyPvuu8/GkTM9D9JOnTrVrqFgy1fVqBZECygv3N0qx0QeOvRKYhpzvLQl07xv2DOuWjMvX9wgKGPISQPqwkwMmT59uuy3336ZK8JrqhnkuwvpMxw9snJDr8Muabxg9gpTEWl5xRpR7wNkZD50d7ySkJss/KYwY6DH+PHjbWEEvBQ+vk260E7gbranTzWDtKBBb8qUKeadAE+zasj/SkKvJI4RI0Z5I/aFYsSocMQkjhGjwhGTOEaMCkdM4hgxKhwxiWPEqGiI/H9EfI+ovciQgQAAAABJRU5ErkJggg==[/img][/center][justify]Nesse sentido, Heron de Alexandria foi um estudioso e inventor da antiguidade, que teve seu trabalho refletivo em várias áreas das ciências exatas e, acima de tudo, na geometria. A [b]Fórmula de Heron[/b] é uma equação usada para calcular a área de um triângulo em que são conhecidos os comprimentos de seus três lados. A fórmula é dada por:[/justify][center]Área = [math]\sqrt{p\cdot\left(p-a\right)\cdot\left(p-b\right)\cdot\left(p-c\right)}[/math][/center][br][justify]onde "[math]a[/math]", "[math]b[/math]" e "[math]c[/math]" são os comprimentos dos lados e "[math]p[/math]" é o semi-perímetro do triângulo (metade da soma dos comprimentos dos lados), ou seja:[/justify] [br][center][math]p=\frac{a+b+c}{2}[/math][/center][br][justify]Interessante notar que, na [b]Fórmula de Heron[/b] não há a necessidade de se conhecer a medida da altura ([math]h[/math]), por isso, quando essa informação não é dada, o "Teorema de Heron" facilita encontrar a área do triângulo.[/justify]
DEMONSTRAÇÃO DA FÓRMULA:
[size=150]A fim de visualizarmos a aplicação da Fórmula de Heron, interaja com o applet seguinte para descobrir a área do triângulo ABC:[/size]
APLICAÇÃO DA FÓRMULA:
ATIVIDADES DE FIXAÇÃO:
[b]1) Qual é o valor da área do triângulo de cujos vértices A, B e C estão associados aos pontos (0,4), (-3,0) e (5,0), respectivamente? [/b](Utilize o applet para encontrar a resposta)
[b]2) Se um triângulo ABC tem os lados a, b e c medindo, respectivamente, 12cm, 13cm e 5cm, qual é a área deste triângulo?[/b]
[b]3) Um triângulo ABC tem área igual a 24cm² e os lados a e b iguais a 8cm e 10cm, respectivamente, qual é a medida do lado c do triângulo?[/b]
[b]4) Se o perímetro de um triângulo ABC é igual a 16cm, sendo que um de seus lados mede 6cm e os outros dois possuem o mesmo comprimento, qual é a área do triângulo ABC?[/b]
[b]5) A Fórmula de Heron pode ser utilizada para qualquer tipo de triângulo (Isósceles, Equilátero, Escaleno)?[/b]
Zavřít

Informace: FÓRMULA DE HERON