STEP 1: find side $ a $

To find side $ a $ use Pythagorean Theorem:

$$ h^2 + \frac{ a^2 }{ 4 } = s^2 $$

After substituting $h = 24\, \text{cm}$ and $s = 25\, \text{cm}$ we have:

$$ \left( 24\, \text{cm} \right)^{2} + \frac{ a^2 }{ 4 } = \left( 25\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = \left( 25\, \text{cm} \right)^{2} - \left( 24\, \text{cm} \right)^{2} $$ $$ \frac{ a^2 }{ 4 } = 625\, \text{cm}^2 - 576\, \text{cm}^2 $$ $$ a^2 = 49\, \text{cm}^2 \cdot 4 $$ $$ a^2 = 196\, \text{cm}^2 $$ $$ a = \sqrt{ 196\, \text{cm}^2 } $$$$ a = 14\, \text{cm} $$

STEP 2: find lateral edge $ e $

To find lateral edge $ e $ use Pythagorean Theorem:

$$ s^2 + \frac{ a^2 }{ 4 } = e^2 $$

After substituting $s = 25\, \text{cm}$ and $a = 14\, \text{cm}$ we have:

$$ \left( 25\, \text{cm} \right)^{2} + \frac{ \left( 14\, \text{cm} \right)^{2} }{ 4 }= e^2 $$ $$ 625\, \text{cm}^2 + \frac{ 196\, \text{cm}^2 }{ 4 }= e^2 $$ $$ 625\, \text{cm}^2 + 49\, \text{cm}^2 = e^2 $$ $$ e^2 = 674\, \text{cm}^2 $$ $$ e = \sqrt{ 674\, \text{cm}^2 } $$$$ e = \sqrt{ 674 }\, \text{cm} $$

Pyramid Calculator