Find the base area $ B $ of a triangular prism if height $h = 6$ and volume $V = 28$.

$B = 12 \sqrt{ 3 }$

STEP 1: find side $ a $

To find side $ a $ use formula:

$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$

After substituting $ h = 6 $ we have:

$$ 6 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 6 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 12 $$ $$ a = \dfrac{ 12 }{ \sqrt{ 3 } } $$ $$ a = 4 \sqrt{ 3 } $$

STEP 2: find base area $ B $

To find base area $ B $ use formula:

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

After substituting $ a = 4 \sqrt{ 3 } $ we have:

$$ B = \dfrac{ \sqrt{ 3 } \cdot \left(4 \sqrt{ 3 }\right)^2 }{ 4 } $$ $$ B = \dfrac{ \sqrt{ 3 } \cdot 48 }{ 4 }$$ $$ B = \dfrac{ 48 \sqrt{ 3 } }{ 4 }$$ $$ B = 12 \sqrt{ 3 } $$

Triangular Prism Calculator