STEP 1: find base diagonal $ d $

To find base diagonal $ d $ use Pythagorean Theorem:

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

After substituting $h = 6\, \text{cm}$ and $e = 12\, \text{cm}$ we have:

$$ \left( 6\, \text{cm} \right)^{2} + \frac{ d^2 }{ 4 } = \left( 12\, \text{cm} \right)^{2} $$ $$ \frac{ d^2 }{ 4 } = \left( 12\, \text{cm} \right)^{2} - \left( 6\, \text{cm} \right)^{2} $$ $$ \frac{ d^2 }{ 4 } = 144\, \text{cm}^2 - 36\, \text{cm}^2 $$ $$ d^2 = 108\, \text{cm}^2 \cdot 4 $$ $$ d^2 = 432\, \text{cm}^2 $$ $$ d = \sqrt{ 432\, \text{cm}^2 } $$$$ d = 12 \sqrt{ 3 }\, \text{cm} $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $d = 12 \sqrt{ 3 }\, \text{cm}$ we have:

$$ 12 \sqrt{ 3 }\, \text{cm} = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 12 \sqrt{ 3 }\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a = 6 \sqrt{ 6 }\, \text{cm} $$

STEP 3: find base area $ B $

To find base area $ B $ use formula:

$$ B = a^2 $$

After substituting $a = 6 \sqrt{ 6 }\, \text{cm}$ we have:

$$ B = \left( 6 \sqrt{ 6 }\, \text{cm} \right)^{2} $$ $$ B = 216\, \text{cm}^2 $$

Pyramid Calculator