Find the area $ A $ of a rhombus if side $a = 26$ and diagonal $d_1 = 48$.
Answer
$A = 480$
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 = 48 $ and $ a = 26 $ we have:
$$ 48^2 + d_2^2 = 4 \cdot 26^2 $$ $$ 2304 + d_2^2 = 2704 $$ $$ d_2^2 = 2704 - 2304 $$ $$ d_2^2 = 400 $$ $$ d_2 = \sqrt{ 400 } $$$$ d_2 = 20 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 48 $ and $ d_2 = 20 $ we have:
$$ A = \dfrac{ 48 \cdot 20 }{ 2 }$$$$ A = \dfrac{ 960 }{ 2 } $$$$ A = 480 $$This page was created using
Rhombus Calculator