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 area $ A $

To find area $ A $ use formula:

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

After substituting $a = 4.8056\, \text{cm}^0$ and $l = 9\, \text{cm}$ we have:

$$ A = \frac{ 4.8056^2 \sqrt{3}}{2} + 3 \cdot 4.8056 \cdot 9\, \text{cm} $$$$ A = \frac{ 23.094 \sqrt{3}}{2} + 3 \cdot 43.2506\, \text{cm} $$$$ A = \frac{ 40}{2} + 129.7518\, \text{cm} $$$$ A = 20 + 129.7518\, \text{cm} $$$$ A = 149.7518 $$

Triangular Prism Calculator