Find the height $ h $ of a pyramid if lateral edge $e = 10$ and base area $B = 1.5$.

$h = 9.9624$

STEP 1: find side $ a $

To find side $ a $ use formula:

After substituting $ B = 1.5 $ we have:

$$ B = a^2 $$ $$ a^2 = 1.5 $$ $$ a = \sqrt{ 1.5 } $$$$ a \approx 1.2247 $$

STEP 2: find base diagonal $ d $

To find base diagonal $ d $ use formula:

$$ d = \sqrt{ 2 } \cdot a $$

After substituting $ a = 1.2247 $ we have:

$$ d = \sqrt{ 2 } \cdot 1.2247 $$ $$ d \approx 1.7321 $$

STEP 3: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + \frac{ d^2 }{ 4 } = e^2 $$

After substituting $ d = 1.7321 $ and $ e = 10 $ we have:

$$ h ^ {\,2} + \frac{ 1.7321^2 }{ 4 } = 10^2 $$ $$ h ^ {\,2} + \frac{ 3 }{ 4 } = 10^2 $$ $$ h ^ {\,2} + 0.75 = 10^2 $$ $$ h ^ {\,2} = 100 - 0.75 $$ $$ h ^ {\,2} = 99.25 $$ $$ h = \sqrt{ 99.25 } $$$$ h = 9.9624 $$

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