STEP 1: find side $ b $

To find side $ b $ use Pythagorean Theorem:

$$ a^2 + b^2 = d^2 $$

After substituting $a = 5\, \text{cm}$ and $d = 9\, \text{cm}$ we have:

$$ \left( 5\, \text{cm} \right)^{2} + b^2 = \left( 9\, \text{cm} \right)^{2} $$ $$ b^2 = \left( 9\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ b^2 = 81\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ b^2 = 56\, \text{cm}^2 $$ $$ b = \sqrt{ 56\, \text{cm}^2 } $$$$ b = 2 \sqrt{ 14 }\, \text{cm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = a \cdot b $$

After substituting $a = 5\, \text{cm}$ and $b = 2 \sqrt{ 14 }\, \text{cm}$ we have:

$$ A = 5\, \text{cm} \cdot 2 \sqrt{ 14 }\, \text{cm} $$$$ A = 5\, \text{cm} \cdot 2 \sqrt{ 14 }\, \text{cm} $$$$ A = 10 \sqrt{ 14 }\, \text{cm}^2 $$

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