Find the area $ A $ of a rhombus if side $a = 13$ and diagonal $d_2 = 10$.
Answer
$A = 120$
Explanation
STEP 1: find diagonal $ d1 $
To find diagonal $ d1 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_2 = 10 $ and $ a = 13 $ we have:
$$ d_1 ^ {\,2} + 10^2 = 4 \cdot 13^2 $$ $$ d_1 ^ {\,2} + 100 = 676 $$ $$ d_1 ^ {\,2} = 676 - 100 $$ $$ d_1 ^ {\,2} = 576 $$ $$ d_1 = \sqrt{ 576 } $$$$ d_1 = 24 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 24 $ and $ d_2 = 10 $ we have:
$$ A = \dfrac{ 24 \cdot 10 }{ 2 }$$$$ A = \dfrac{ 240 }{ 2 } $$$$ A = 120 $$This page was created using
Rhombus Calculator