STEP 1: find side $ a $

To find side $ a $ use formula:

$$ r = \dfrac{ a }{ 2 } $$

After substituting $r = 45.822\, \text{cm}$ we have:

$$ 45.822\, \text{cm} = \dfrac{ a }{ 2 } $$ $$ a = 45.822\, \text{cm} \cdot 2 $$ $$ a = 91.644\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $a = 91.644\, \text{cm}$ and $s = 68.479\, \text{cm}$ we have:

$$ h ^ {\,2} + \frac{ \left( 91.644\, \text{cm} \right)^{2} }{ 4 } = \left( 68.479\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + \frac{ 8398.6227\, \text{cm}^2 }{ 4 } = \left( 68.479\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} + 2099.6557\, \text{cm}^2 = \left( 68.479\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 4689.3734\, \text{cm}^2 - 2099.6557\, \text{cm}^2 $$ $$ h ^ {\,2} = 2589.7178\, \text{cm}^2 $$ $$ h = \sqrt{ 2589.7178\, \text{cm}^2 } $$$$ h = 50.8893\, \text{cm} $$

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