STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 18 $ and $ b = 8 $ we have:
$$ x = \frac{ 18 - 8 } { 2 } $$ $$ x = \frac{ 10 } { 2 } $$ $$ x = 5 $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ x = 5 $ and $ c = 4 \sqrt{ 3 } $ we have:
$$ h ^ {\,2} + 5^2 = \left(4 \sqrt{ 3 }\right)^2 $$ $$ h ^ {\,2} = \left(4 \sqrt{ 3 }\right)^2 - 5^2 $$ $$ h ^ {\,2} = 48 - 25 $$ $$ h ^ {\,2} = 23 $$ $$ h = \sqrt{ 23 } $$STEP 3: find area $ A $
To find area $ A $ use formula:
$$ A = \frac{ (a + b) \cdot h}{ 2 }$$After substituting $ a = 18 $ , $ b = 8 $ and $ h = \sqrt{ 23 } $ we have:
$$ A = \frac{ (18 + 8) \cdot \sqrt{ 23 }}{ 2 }$$$$ A = \frac{ 26 \cdot \sqrt{ 23 }}{ 2 }$$$$ A = \frac{ 26 \sqrt{ 23 } }{ 2 }$$ $$ A = 13 \sqrt{ 23 } $$