STEP 1: find side $ a $

To find side $ a $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $h = 7.8\, \text{cm}$ we have:

$$ 7.8\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 7.8\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 15.6\, \text{cm} $$ $$ a = \dfrac{ 15.6\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a \approx 9.0067\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \frac{ a^2 \sqrt{3}}{2} + 3 a l $$

After substituting $a = 9.0067\, \text{cm}$ and $l = 12\, \text{cm}$ we have:

$$ A = \frac{ 9.0067\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 9.0067\, \text{cm} \cdot 12\, \text{cm} $$$$ A = \frac{ 81.12\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 108.08\, \text{cm}^2 $$$$ A = \frac{ 140.504\, \text{cm}^2}{2} + 324.2399\, \text{cm}^2 $$$$ A = 70.252\, \text{cm}^2 + 324.2399\, \text{cm}^2 $$$$ A = 394.4919\, \text{cm}^2 $$

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