Find the area $ A $ of a rhombus if side $a = 5$ and diagonal $d_1 = 6$.
Answer
$A = 24$
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 = 6 $ and $ a = 5 $ we have:
$$ 6^2 + d_2^2 = 4 \cdot 5^2 $$ $$ 36 + d_2^2 = 100 $$ $$ d_2^2 = 100 - 36 $$ $$ d_2^2 = 64 $$ $$ d_2 = \sqrt{ 64 } $$$$ d_2 = 8 $$STEP 2: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 6 $ and $ d_2 = 8 $ we have:
$$ A = \dfrac{ 6 \cdot 8 }{ 2 }$$$$ A = \dfrac{ 48 }{ 2 } $$$$ A = 24 $$This page was created using
Rhombus Calculator