STEP 1: find side $ x $

To find side $ x $ use formula:

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

After substituting $a = 18\, \text{cm}$ and $b = 8\, \text{cm}$ we have:

$$ x = \frac{ 18\, \text{cm} - 8\, \text{cm} } { 2 } $$ $$ x = \frac{ 10\, \text{cm} } { 2 } $$ $$ x = 5\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $x = 5\, \text{cm}$ and $c = 4 \sqrt{ 3 }\, \text{cm}$ we have:

$$ h ^ {\,2} + \left( 5\, \text{cm} \right)^{2} = \left( 4 \sqrt{ 3 }\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = \left( 4 \sqrt{ 3 }\, \text{cm} \right)^{2} - \left( 5\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 48\, \text{cm}^2 - 25\, \text{cm}^2 $$ $$ h ^ {\,2} = 23\, \text{cm}^2 $$ $$ h = \sqrt{ 23\, \text{cm}^2 } $$$$ h = \sqrt{ 23 }\, \text{cm} $$

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:

$$ A = \frac{ (18\, \text{cm} + 8\, \text{cm}) \cdot \sqrt{ 23 }\, \text{cm}}{ 2 }$$$$ A = \frac{ 26\, \text{cm} \cdot \sqrt{ 23 }\, \text{cm}}{ 2 }$$$$ A = \frac{ 26 \sqrt{ 23 }\, \text{cm}^2 }{ 2 }$$ $$ A = 13 \sqrt{ 23 }\, \text{cm}^2 $$

Trapezoid Calculator