STEP 1: find side $ a $
To find side $ a $ use formula:
$$ P = 4 \cdot a $$After substituting $ P = 52 $ we have:
$$ 52 = 4 \cdot a $$ $$ a = \dfrac{ 52 }{ 4 } $$ $$ a = 13 $$STEP 2: find diagonal $ d2 $
To find diagonal $ d2 $ use formula:
$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$After substituting $ d_1 = 10 $ and $ a = 13 $ we have:
$$ 10^2 + d_2^2 = 4 \cdot 13^2 $$ $$ 100 + d_2^2 = 676 $$ $$ d_2^2 = 676 - 100 $$ $$ d_2^2 = 576 $$ $$ d_2 = \sqrt{ 576 } $$$$ d_2 = 24 $$STEP 3: find area $ A $
To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 10 $ and $ d_2 = 24 $ we have:
$$ A = \dfrac{ 10 \cdot 24 }{ 2 }$$$$ A = \dfrac{ 240 }{ 2 } $$$$ A = 120 $$