Answer
$A\approx11.3cm^{2}$
Work Step by Step
$$a^{2}+b^{2}=c^{2}$$
$1^{2}+b^{2}=3^{2}$
$1+b^{2}=9$
$b^{2}=8$
$b=2\sqrt 2$
$b=2.828$
To find the height of the trapezoid, use the Pythagorean theorem with the two lengths of the triangle provided:
$$A=\frac{1}{2}(b_{1}+b_{2})h$$
$A=\frac{1}{2}(5+3)2.828$
$A=11.312$
$A=11.3 cm^{2}$
To find the area of the trapezoid, use the trapezoid area formula and plug in the height of the triangle we found previously. Following that, solve for A.
