STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 24 $ and $ b = 14 $ we have:
$$ x = \frac{ 24 - 14 } { 2 } $$ $$ x = \frac{ 10 } { 2 } $$ $$ x = 5 $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ x = 5 $ and $ c = 9 $ we have:
$$ h ^ {\,2} + 5^2 = 9^2 $$ $$ h ^ {\,2} = 9^2 - 5^2 $$ $$ h ^ {\,2} = 81 - 25 $$ $$ h ^ {\,2} = 56 $$ $$ h = \sqrt{ 56 } $$$$ h = 2 \sqrt{ 14 } $$STEP 3: find area $ A $
To find area $ A $ use formula:
$$ A = \frac{ (a + b) \cdot h}{ 2 }$$After substituting $ a = 24 $ , $ b = 14 $ and $ h = 2 \sqrt{ 14 } $ we have:
$$ A = \frac{ (24 + 14) \cdot 2 \sqrt{ 14 }}{ 2 }$$$$ A = \frac{ 38 \cdot 2 \sqrt{ 14 }}{ 2 }$$$$ A = \frac{ 76 \sqrt{ 14 } }{ 2 }$$ $$ A = 38 \sqrt{ 14 } $$