Find the area $ A $ of a rhombus if side $a = 42290$ and diagonal $d_1 = 53173$.

$A = \frac{ 1010287 \sqrt{ 11984511}}{ 2 }$

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 = 53173 $ and $ a = 42290 $ we have:

$$ 53173^2 + d_2^2 = 4 \cdot 42290^2 $$ $$ 2827367929 + d_2^2 = 7153776400 $$ $$ d_2^2 = 7153776400 - 2827367929 $$ $$ d_2^2 = 4326408471 $$ $$ d_2 = \sqrt{ 4326408471 } $$$$ d_2 = 19 \sqrt{ 11984511 } $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = 53173 $ and $ d_2 = 19 \sqrt{ 11984511 } $ we have:

$$ A = \dfrac{ 53173 \cdot 19 \sqrt{ 11984511 } }{ 2 }$$$$ A = \dfrac{ 1010287 \sqrt{ 11984511 } }{ 2 } $$$$ A = \frac{ 1010287 \sqrt{ 11984511}}{ 2 } $$

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