## Geometry: Common Core (15th Edition)

$A\approx11.3cm^{2}$
$$a^{2}+b^{2}=c^{2}$$ $1^{2}+b^{2}=3^{2}$ $1+b^{2}=9$ $b^{2}=8$ $b=2\sqrt 2$ $b=2.828$ 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.