Answer:
S = 3.97 cm^2
Step-by-step explanation:
The given shape is a trapezoid. Since it's a right trapezoid, then the leg that's perpendicular to both bases of the trapezoids acts as the height.
The formula for a trapezoid's area is:
[tex]S = \frac{(a + b)h}2[/tex]
Where a and b are the lengths of the trapezoid's bases and h is the height of the trapezoid (the length of a line that's perpendicular to both bases).
In this problem, a = sqrt(10), b = sqrt(6), c = sqrt(2).
[tex]S = \frac{(\sqrt{10} + \sqrt6)\sqrt2}2\\\\\to S = \frac{\sqrt{10} + \sqrt6}{\sqrt2}\\\\\to S = \frac{\sqrt2(\sqrt{5} + \sqrt{3})}{\sqrt2}\\\\\to S = \sqrt5 + \sqrt3\approx 3.97[/tex]
The area of the trapezoid is, approximately, 3.97 cm^2.
