Question
Find the lateral area $ L $ of a pyramid if slant height $s = 7.6\, \text{cm}$ and base diagonal $d = 6.7\, \text{cm}$.
Answer
$72.0118\, \text{cm}^2$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $d = 6.7\, \text{cm}$ we have:
$$ 6.7\, \text{cm} = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ 6.7\, \text{cm} }{ \sqrt{ 2 } } $$ $$ a \approx 4.7376\, \text{cm} $$STEP 2: find lateral surface $ L $
To find lateral surface $ L $ use formula:
$$ L = 2 \cdot a \cdot s $$After substituting $a = 4.7376\, \text{cm}$ and $s = 7.6\, \text{cm}$ we have:
$$ L = 9.4752\, \text{cm} \cdot 7.6\, \text{cm} $$$$ L = 72.0118\, \text{cm}^2 $$This page was created using
Pyramid Calculator