Question

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

Answer 1

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

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