Find the area $ A $ of a rhombus if side $a = 9$ and diagonal $d_2 = 2$.
Answer
$A = 8 \sqrt{ 5 }$
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 = 2 $ and $ a = 9 $ we have:
$$ d_1 ^ {\,2} + 2^2 = 4 \cdot 9^2 $$ $$ d_1 ^ {\,2} + 4 = 324 $$ $$ d_1 ^ {\,2} = 324 - 4 $$ $$ d_1 ^ {\,2} = 320 $$ $$ d_1 = \sqrt{ 320 } $$$$ d_1 = 8 \sqrt{ 5 } $$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{ 5 } $ and $ d_2 = 2 $ we have:
$$ A = \dfrac{ 8 \sqrt{ 5 } \cdot 2 }{ 2 }$$$$ A = \dfrac{ 16 \sqrt{ 5 } }{ 2 } $$$$ A = 8 \sqrt{ 5 } $$This page was created using
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