Calcula el área de la región rombal ABCD de perímetro 60m.

Adjuntos:

Respuestas

Respuesta dada por: Meganium123
8

Explicación paso a paso:

Usando Pitágoras Determinamos BH

 {(BH)}^{2}  =   {(5a)}^{2}  - {(4a)}^{2}  \\ {(BH)}^{2}  =   {25a}^{2}  - {16a}^{2}  \\ {(BH)}^{2}  =   {9a}^{2}   \\ (BH)=  \sqrt{{9a}^{2}}  \\  \boxed{(BH)=  3a}

Hallando la Region Sombreada.

As = 2(AreaABH) + 2(AreaBHD)

As = 2(AreaABH) + 2(AreaBHD) \\ As = 2( \frac{4 a\times 3a}{2} ) + 2( \frac{a \times 3a}{2} ) \\ As =  12 {a}^{2}  + 3 {a}^{2}  \\  \boxed{As =  15 {a}^{2}  }

Hallando el valor de "a"

P = 4(5a)\\60 = 20a\\ a = \frac{60}{20}\\ \boxed{a=3}

Reemplazando en As

As =  15 {a}^{2} \\As =  15 {(3)}^{2}\\ As =  15 (9)\\ \boxed{As =  135}

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