[tex]de = \sqrt{(5 + 1) {}^{2} + (3 + 1) {}^{2} } = \sqrt{ {6}^{2} + 4 {}^{2} } = \sqrt{36 + 16} = \sqrt{52} = 2 \sqrt{13} [/tex]
[tex]ef = \sqrt{(7 - 5) {}^{2} + (0 - 3) {}^{2} } = \sqrt{ {2}^{2} + ( -3) {}^{2} } = \sqrt{4 + 9} = \sqrt{13} [/tex]
[tex]df = \sqrt{(7 + 1) {}^{2} + (0 + 1) {}^{2} } = \sqrt{8 {}^{2} + {1}^{2} } = \sqrt{64 + 1} = \sqrt{65} [/tex]
DE=4•13=52
EF=13
DF=65
DE+EF=52+13=65=> triunghiul DEF este dreptunghic
A(DEF)=DE•EF/2
[tex]A(DEF) = 2 \sqrt{13 } \times \sqrt{13} \div 2 = 13[/tex]
A(DEF)=13 cm^2
