STEP 1: find side $ a $

To find side $ a $ use formula:

$$ B = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$

After substituting $B = 3.4\, \text{cm}$ we have:

$$ 3.4\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a^2 }{ 4 }$$ $$ 3.4\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot a^2 $$ $$ 13.6\, \text{cm} = \sqrt{ 3 } \cdot a^2 $$ $$ a^2 = \dfrac{ 13.6\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a^2 = 7.852\, \text{cm} $$ $$ a = \sqrt{ 7.852\, \text{cm} } $$$$ a \approx 2.8021 $$

STEP 2: find length $ l $

To find length $ l $ use formula:

$$ V = \dfrac{ \sqrt{ 3 } \cdot a ^{ 2 } \cdot l }{ 4 } $$

After substituting $V = 1.7918\, \text{cm}$ and $a = 2.8021\, \text{cm}^0$ we have:

$$ 1.7918\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot 2.8021 ^{ 2 } \cdot l }{ 4 } $$$$ 1.7918\, \text{cm} \cdot 4 = \sqrt{ 3 } \cdot 2.8021 ^{ 2 } \cdot l $$$$ 7.1672\, \text{cm} = \sqrt{ 3 } \cdot 2.8021 ^{ 2 } \cdot l $$$$ 7.1672\, \text{cm} = 13.6 \cdot l $$$$ l = \dfrac{ 7.1672\, \text{cm} }{ 13.6 } $$$$ l = 0.527\, \text{cm} $$

STEP 3: find area $ A $

To find area $ A $ use formula:

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

After substituting $a = 2.8021\, \text{cm}^0$ and $l = 0.527\, \text{cm}$ we have:

$$ A = \frac{ 2.8021^2 \sqrt{3}}{2} + 3 \cdot 2.8021 \cdot 0.527\, \text{cm} $$$$ A = \frac{ 7.852 \sqrt{3}}{2} + 3 \cdot 1.4767\, \text{cm} $$$$ A = \frac{ 13.6}{2} + 4.4302\, \text{cm} $$$$ A = 6.8 + 4.4302\, \text{cm} $$$$ A = 11.2302 $$

Triangular Prism Calculator