Find the base area $ B $ of a triangular prism if height $h = 8.7$ and lateral $AL = 12$.

$B = 43.6996$

STEP 1: find side $ a $

To find side $ a $ use formula:

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

After substituting $ h = 8.7 $ we have:

$$ 8.7 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 8.7 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 17.4 $$ $$ a = \dfrac{ 17.4 }{ \sqrt{ 3 } } $$ $$ a \approx 10.0459 $$

STEP 2: find base area $ B $

To find base area $ B $ use formula:

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

After substituting $ a = 10.0459 $ we have:

$$ B = \dfrac{ \sqrt{ 3 } \cdot 10.0459^2 }{ 4 } $$ $$ B = \dfrac{ \sqrt{ 3 } \cdot 100.92 }{ 4 }$$ $$ B = \dfrac{ 174.7986 }{ 4 }$$ $$ B = 43.6996 $$

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