STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 910 $ and $ b = 500 $ we have:
$$ x = \frac{ 910 - 500 } { 2 } $$ $$ x = \frac{ 410 } { 2 } $$ $$ x = 205 $$STEP 2: find height $ h $
To find height $ h $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ x = 205 $ and $ c = \frac{ 899 }{ 2 } $ we have:
$$ h ^ {\,2} + 205^2 = \left(\frac{ 899 }{ 2 }\right)^2 $$ $$ h ^ {\,2} = \left(\frac{ 899 }{ 2 }\right)^2 - 205^2 $$ $$ h ^ {\,2} = \frac{ 808201 }{ 4 } - 42025 $$ $$ h ^ {\,2} = \frac{ 640101 }{ 4 } $$ $$ h = \sqrt{ \frac{ 640101 }{ 4 } } $$$$ h = \frac{\sqrt{ 640101 }}{ 2 } $$STEP 3: find area $ A $
To find area $ A $ use formula:
$$ A = \frac{ (a + b) \cdot h}{ 2 }$$After substituting $ a = 910 $ , $ b = 500 $ and $ h = \frac{\sqrt{ 640101 }}{ 2 } $ we have:
$$ A = \frac{ (910 + 500) \cdot \frac{\sqrt{ 640101 }}{ 2 }}{ 2 }$$$$ A = \frac{ 1410 \cdot \frac{\sqrt{ 640101 }}{ 2 }}{ 2 }$$$$ A = \frac{ 705 \sqrt{ 640101 } }{ 2 }$$ $$ A = \frac{ 705 \sqrt{ 640101}}{ 2 } $$