Find the base area $ B $ of a triangular prism if length $l = 9.9$ and height $h = 7.2$.

$B = 29.9298$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 7.2 $ we have:

$$ 7.2 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 7.2 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 14.4 $$ $$ a = \dfrac{ 14.4 }{ \sqrt{ 3 } } $$ $$ a \approx 8.3138 $$

STEP 2: find base area $ B $

To find base area $ B $ use formula:

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

After substituting $ a = 8.3138 $ we have:

$$ B = \dfrac{ \sqrt{ 3 } \cdot 8.3138^2 }{ 4 } $$ $$ B = \dfrac{ \sqrt{ 3 } \cdot 69.12 }{ 4 }$$ $$ B = \dfrac{ 119.7194 }{ 4 }$$ $$ B = 29.9298 $$

Triangular Prism Calculator