To find area $ A $ use formula:

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

After substituting $a = 10\, \text{cm}$ and $l = 13\, \text{cm}$ we have:

$$ A = \frac{ 10\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 10\, \text{cm} \cdot 13\, \text{cm} $$$$ A = \frac{ 100\, \text{cm}^2 \sqrt{3}}{2} + 3 \cdot 130\, \text{cm}^2 $$$$ A = \frac{ 100 \sqrt{ 3 }\, \text{cm}^2}{2} + 390\, \text{cm}^2 $$$$ A = 50 \sqrt{ 3 }\, \text{cm}^2 + 390\, \text{cm}^2 $$$$ A = 476.6025\, \text{cm}^2 $$

Triangular Prism Calculator