STEP 1: find width $ w $

To find width $ w $ use formula:

$$ d^2 = l^2 + w^2 + h^2 $$

After substituting $d = 6\, \text{mm}$, $l = 5\, \text{mm}$ and $h = 1.2\, \text{mm}$ we have:

$$ 6\, \text{mm}^2 = 5\, \text{mm}^2 + w^2 + 1.2\, \text{mm}^2 $$$$ 36\, \text{mm}^2 = 25\, \text{mm}^2 + w^2 + 1.44\, \text{mm}^2 $$$$ 36\, \text{mm}^2 = w^2 + 26.44\, \text{mm}^2 $$$$ w^2 = 36\, \text{mm}^2 - 26.44\, \text{mm}^2 $$ $$ w^2 = 9.56\, \text{mm}^2 $$ $$ w = \sqrt{ 9.56\, \text{mm}^2 } $$$$ w = 3.0919\, \text{mm} $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

$$ V = l \cdot w \cdot h $$

After substituting $l = 5\, \text{mm}$, $w = 3.0919\, \text{mm}$ and $h = 1.2\, \text{mm}$ we have:

$$ V = 5\, \text{mm} \cdot 3.0919\, \text{mm} \cdot 1.2\, \text{mm} $$$$ V = 15.4596\, \text{mm}^2 \cdot 1.2\, \text{mm} $$ $$ V = 18.5515\, \text{mm}^3 $$

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