STEP 1: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $A = 36\, \text{cm}$ and $d_1 = 8\, \text{cm}$ we have:

$$ 36\, \text{cm} = \dfrac{ 8\, \text{cm} \cdot d_2 }{ 2 } $$$$ 36\, \text{cm} \cdot 2 = 8\, \text{cm} \cdot d_2 $$$$ 72\, \text{cm} = 8\, \text{cm} \cdot d_2 $$$$ d_2 = \dfrac{ 72\, \text{cm} }{ 8\, \text{cm} } $$$$ d_2 = 9 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $d_1 = 8\, \text{cm}$ and $d_2 = 9\, \text{cm}^0$ we have:

$$ \left( 8\, \text{cm} \right)^{2} + 9 = 4 \cdot a^2 $$ $$ 64\, \text{cm}^2 + 81 = 4 \cdot a^2 $$ $$ 4 \cdot a^2 = 145\, \text{cm}^2 $$ $$ a^2 = \frac{ 145\, \text{cm}^2 }{ 4 } $$ $$ a^2 = \frac{ 145 }{ 4 }\, \text{cm}^2 $$ $$ a = \sqrt{ \frac{ 145 }{ 4 }\, \text{cm}^2 } $$$$ a = \frac{\sqrt{ 145 }}{ 2 }\, \text{cm} $$

Rhombus Calculator