Find the area $ A $ of a rhombus if side $a = 11$ and diagonal $d_1 = 2$.
Answer
$A = 4 \sqrt{ 30 }$
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 = 2 $ and $ a = 11 $ we have:
$$ 2^2 + d_2^2 = 4 \cdot 11^2 $$ $$ 4 + d_2^2 = 484 $$ $$ d_2^2 = 484 - 4 $$ $$ d_2^2 = 480 $$ $$ d_2 = \sqrt{ 480 } $$$$ d_2 = 4 \sqrt{ 30 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 2 $ and $ d_2 = 4 \sqrt{ 30 } $ we have:
$$ A = \dfrac{ 2 \cdot 4 \sqrt{ 30 } }{ 2 }$$$$ A = \dfrac{ 8 \sqrt{ 30 } }{ 2 } $$$$ A = 4 \sqrt{ 30 } $$This page was created using
Rhombus Calculator