Respuestas

2013-09-28T05:37:35+02:00
Aplicamos el teorema de Heron.

Area= \sqrt{P(P-A)(P-B)(P-C)}

Lados: A = 6 ; B =  2\sqrt{5} ; C = 4

Perimetro: 2P = 6+2 \sqrt{5}+4=10+2 \sqrt{5} =2(5+ \sqrt{5})

Semiperimetro: P= \frac{2(5+ \sqrt{5} )}{2} =5+ \sqrt{5}

Reemplazamos los datos en la formula de Heron:

Area= \sqrt{(5+ \sqrt{5})(5+ \sqrt{5}-6)(5+ \sqrt{5}-2\sqrt{5})(5+ \sqrt{5}-4)}

Area= \sqrt{(5+ \sqrt{5})(\sqrt{5}-1)(5-\sqrt{5})(1+ \sqrt{5})}

Area= \sqrt{[(5+ \sqrt{5})(5-\sqrt{5})][(\sqrt{5}+1)(\sqrt{5}-1)]}

Area= \sqrt{[5^{2} - \sqrt{5}^{2} ][\sqrt{5}^{2} -1^{2}]}

Area= \sqrt{[25 - 5][5 -1]}

Area= \sqrt{[20][4]}

Area= \sqrt{80}

Area= 4\sqrt{5}