Find the area $ A $ of a rhombus if side $a = 10$ and diagonal $d_2 = 4$.
Answer
$A = 16 \sqrt{ 6 }$
Explanation
STEP 1: find diagonal $ d1 $
To find diagonal $ d1 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_2 = 4 $ and $ a = 10 $ we have:
$$ d_1 ^ {\,2} + 4^2 = 4 \cdot 10^2 $$ $$ d_1 ^ {\,2} + 16 = 400 $$ $$ d_1 ^ {\,2} = 400 - 16 $$ $$ d_1 ^ {\,2} = 384 $$ $$ d_1 = \sqrt{ 384 } $$$$ d_1 = 8 \sqrt{ 6 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 8 \sqrt{ 6 } $ and $ d_2 = 4 $ we have:
$$ A = \dfrac{ 8 \sqrt{ 6 } \cdot 4 }{ 2 }$$$$ A = \dfrac{ 32 \sqrt{ 6 } }{ 2 } $$$$ A = 16 \sqrt{ 6 } $$This page was created using
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