Answer
$158.75\ cm^2$
Work Step by Step
To find the area of the shaded part of the figure, first find the area of the complete rectangle then subtract the area of the triangle that is not shaded.
The area of the rectangle is
$bh=(20\ cm)(10\ cm)=200\ cm^2$
The length of the base of the triangle is not given, but can be found by subtracting the portions of the base of the rectangle that are not part of the triangle.
The area of the triangle is
$\frac{1}{2}bh=\frac{1}{2}(20-4-5\ cm)(7.5\ cm)=\frac{1}{2}(11\ cm)(7.5\ cm)=41.25\ cm^2$
Subtract the area of the triangle from the area of the rectangle to find the shaded area.
$200\ cm^2-41.25\ cm^2=158.75\ cm^2$
