Find the area $ A $ of a rhombus if side $a = 13$ and diagonal $d_1 = 12$.
Answer
$A = 12 \sqrt{ 133 }$
Explanation
STEP 1: find diagonal $ d2 $
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 12 $ and $ a = 13 $ we have:
$$ 12^2 + d_2^2 = 4 \cdot 13^2 $$ $$ 144 + d_2^2 = 676 $$ $$ d_2^2 = 676 - 144 $$ $$ d_2^2 = 532 $$ $$ d_2 = \sqrt{ 532 } $$$$ d_2 = 2 \sqrt{ 133 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 12 $ and $ d_2 = 2 \sqrt{ 133 } $ we have:
$$ A = \dfrac{ 12 \cdot 2 \sqrt{ 133 } }{ 2 }$$$$ A = \dfrac{ 24 \sqrt{ 133 } }{ 2 } $$$$ A = 12 \sqrt{ 133 } $$This page was created using
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