Find the area $ A $ of a cube if body diagonal $d = 5 \sqrt{ 3 }$.
Answer
$A = 150$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 3 } \cdot a $$After substituting $ d = 5 \sqrt{ 3 } $ we have:
$$ 5 \sqrt{ 3 } = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ 5 \sqrt{ 3 } }{ \sqrt{ 3 } } $$ $$ a = 5 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = 6 \cdot a^2 $$After substituting $ a = 5 $ we have:
$$ A = 6 \cdot 5^2 $$ $$ A = 150 $$ $$ A = 150 $$This page was created using
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