Find the area $ A $ of a rhombus if diagonal $d_2 = 9$ and angle $\alpha = 60^o$.

$A = 81$

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 = 30^o $ and $ d_2 = 9 $ we have:

$$ \sin \left( \frac{ 60^o }{ 2 } \right) = \dfrac{ d_2 }{ } $$ $$ \sin( 30^o ) = \dfrac{ 9 }{ d_1 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ 9 }{ d_1 } $$ $$ d_1 = \dfrac{ 9 }{ \frac{ 1 }{ 2 } } $$ $$ d_1 = 18 $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ d_1 = 18 $ and $ d_2 = 9 $ we have:

$$ A = \dfrac{ 18 \cdot 9 }{ 2 }$$$$ A = \dfrac{ 162 }{ 2 } $$$$ A = 81 $$

Rhombus Calculator