Find the area $ A $ of a rhombus if diagonal $d_2 = \frac{ 64 }{ 5 }$ and angle $\alpha = 52^o$.

$A = 186.8736$

STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$

After substituting $ \alpha = 26^o $ and $ d_2 = \frac{ 64 }{ 5 } $ we have:

$$ \sin \left( \frac{ 52^o }{ 2 } \right) = \dfrac{ d_2 }{ } $$ $$ \sin( 26^o ) = \dfrac{ \frac{ 64 }{ 5 } }{ d_1 } $$ $$ 0.4384 = \dfrac{ \frac{ 64 }{ 5 } }{ d_1 } $$ $$ d_1 = \dfrac{ \frac{ 64 }{ 5 } }{ 0.4384 } $$ $$ d_1 = 29.199 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = 29.199 $ and $ d_2 = \frac{ 64 }{ 5 } $ we have:

$$ A = \dfrac{ 29.199 \cdot \frac{ 64 }{ 5 } }{ 2 }$$$$ A = \dfrac{ 373.7472 }{ 2 } $$$$ A = 186.8736 $$

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