STEP 1: find side $ a $

To find side $ a $ use formula:

$$ B = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$

After substituting $B = 10\, \text{cm}$ we have:

$$ 10\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 10\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 40\, \text{cm} = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 40\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a^2 = \frac{ 40 \sqrt{ 3}}{ 3 }\, \text{cm} $$ $$ a = \sqrt{ \frac{ 40 \sqrt{ 3}}{ 3 }\, \text{cm} } $$$$ a \approx 4.8056 $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $a = 4.8056\, \text{cm}^0$ we have:

$$ h = \dfrac{ \sqrt{ 3 } \cdot 4.8056 }{ 2 } $$$$ h = \dfrac{ 8.3236 }{ 2 } $$ $$ h \approx 4.1618 $$

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