Find the area $ A $ of a rhombus if side $a = 20$ and diagonal $d_1 = 36$.
Answer
$A = 72 \sqrt{ 19 }$
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 = 36 $ and $ a = 20 $ we have:
$$ 36^2 + d_2^2 = 4 \cdot 20^2 $$ $$ 1296 + d_2^2 = 1600 $$ $$ d_2^2 = 1600 - 1296 $$ $$ d_2^2 = 304 $$ $$ d_2 = \sqrt{ 304 } $$$$ d_2 = 4 \sqrt{ 19 } $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 36 $ and $ d_2 = 4 \sqrt{ 19 } $ we have:
$$ A = \dfrac{ 36 \cdot 4 \sqrt{ 19 } }{ 2 }$$$$ A = \dfrac{ 144 \sqrt{ 19 } }{ 2 } $$$$ A = 72 \sqrt{ 19 } $$This page was created using
Rhombus Calculator