Find the area $ A $ of a rhombus if side $a = 460$ and diagonal $d_2 = 370$.

$A = 1850 \sqrt{ 7095 }$

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 = 370 $ and $ a = 460 $ we have:

$$ d_1 ^ {\,2} + 370^2 = 4 \cdot 460^2 $$ $$ d_1 ^ {\,2} + 136900 = 846400 $$ $$ d_1 ^ {\,2} = 846400 - 136900 $$ $$ d_1 ^ {\,2} = 709500 $$ $$ d_1 = \sqrt{ 709500 } $$$$ d_1 = 10 \sqrt{ 7095 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $ d_1 = 10 \sqrt{ 7095 } $ and $ d_2 = 370 $ we have:

$$ A = \dfrac{ 10 \sqrt{ 7095 } \cdot 370 }{ 2 }$$$$ A = \dfrac{ 3700 \sqrt{ 7095 } }{ 2 } $$$$ A = 1850 \sqrt{ 7095 } $$

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