STEP 1: find side $ x $

To find side $ x $ use formula:

$$ x = \frac{ a - b } { 2 } $$

After substituting $a = 910\, \text{cm}$ and $b = 500\, \text{cm}$ we have:

$$ x = \frac{ 910\, \text{cm} - 500\, \text{cm} } { 2 } $$ $$ x = \frac{ 410\, \text{cm} } { 2 } $$ $$ x = 205\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

$$ h^2 + x^2 = c^2 $$

After substituting $x = 205\, \text{cm}$ and $c = 449.5\, \text{cm}$ we have:

$$ h ^ {\,2} + \left( 205\, \text{cm} \right)^{2} = \left( 449.5\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = \left( 449.5\, \text{cm} \right)^{2} - \left( 205\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 202050.25\, \text{cm}^2 - 42025\, \text{cm}^2 $$ $$ h ^ {\,2} = 160025.25\, \text{cm}^2 $$ $$ h = \sqrt{ 160025.25\, \text{cm}^2 } $$$$ h = 400.0316\, \text{cm} $$

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 = 400.0316 $ we have:

$$ A = \frac{ (910\, \text{cm} + 500\, \text{cm}) \cdot 400.0316\, \text{cm}}{ 2 }$$$$ A = \frac{ 1410\, \text{cm} \cdot 400.0316\, \text{cm}}{ 2 }$$$$ A = \frac{ 564044.5014\, \text{cm}^2 }{ 2 }$$ $$ A = 282022.2507\, \text{cm}^2 $$

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