Answer
Area $=3\sqrt { 3}$ square feet.
Work Step by Step
Smaller side $b=\sqrt 2$ feet.
Larger side $a=\sqrt 8$ feet.
Distance between parallel sides: $h=\sqrt 6$ feet.
Area $A=\frac{1}{2}h(a+b)$.
Substitute all values.
$\Rightarrow A=\frac{1}{2}(\sqrt 6)(\sqrt 8+\sqrt 2)$.
Factor all terms.
$\Rightarrow A=\frac{1}{2}(\sqrt {2\cdot 3})(\sqrt {2^3}+\sqrt 2)$.
Simplify.
$\Rightarrow A=\frac{1}{2}(\sqrt {2\cdot 3})(2\sqrt {2}+\sqrt 2)$.
$\Rightarrow A=\frac{1}{2}(\sqrt {2\cdot 3})(3\sqrt {2})$.
$\Rightarrow A=\frac{3}{2}\sqrt {2\cdot 3}\cdot \sqrt {2}$.
Multiply the radicands and retain the common index.
$\Rightarrow A=\frac{3}{2}\sqrt {2\cdot 3\cdot 2}$.
$\Rightarrow A=\frac{3}{2}\sqrt {2^2\cdot 3}$.
$\Rightarrow A=\frac{3}{2}\cdot 2\sqrt { 3}$.
Cancel common terms.
$\Rightarrow A=3\sqrt { 3}$ square feet.
