Find the area $ A $ of a square if diagonal $d = \frac{ 73 }{ 5 }$.
Answer
$A = \frac{ 5329 }{ 50 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ d = \sqrt{ 2 } \cdot a $$After substituting $ d = \frac{ 73 }{ 5 } $ we have:
$$ \frac{ 73 }{ 5 } = \sqrt{ 2 } \cdot a $$ $$ a = \dfrac{ \frac{ 73 }{ 5 } }{ \sqrt{ 2 } } $$ $$ a = \frac{ 73 \sqrt{ 2}}{ 10 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = a^2 $$After substituting $ a = \frac{ 73 \sqrt{ 2}}{ 10 } $ we have:
$$ A = \left( \frac{ 73 \sqrt{ 2}}{ 10 } \right)^2 $$ $$ A = \frac{ 5329 }{ 50 } $$This page was created using
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