To find the area of the shaded region we need to divide it into one triangle and two rectangles like you can see in the picture.
The area of a triangle is [tex]A _{t} = \frac{1}{2} (base)(height)[/tex], and we know from our figure that our triangle has base=10 feet and height=5 feet, so:
[tex]A_{t} = \frac{1}{2} (10feet)(5feet)[/tex]
[tex]A_{t} = 25feet^{2} [/tex]
The area of a rectangle is [tex]A_{r} =(length)(width)[/tex]. We have tow rectangles in our figure, so for our first one:
[tex]A _{r1} =(10feet)(1feet)[/tex]
[tex]A_{r1}=10feet^{2} [/tex]
for our second one:
[tex]A_{r2} =(8feet)(2feet)[/tex]
[tex]A_{r2} =16feet^{2} [/tex]
Now that we have the areas of all out figures, lets add them to find the area of the shaded region:
[tex]A _{total} =25feet^{2} +10feet^{2} +16feet^{2} [/tex]
[tex]A _{total} =51feet^{2} [/tex]
We can conclude that the area of the shaded region is 51 square feet.
