For this case we have that the area of the figure is given by the sum of the area of a rectangle plus the area of a triangle.
By definition, the area of a reactangle is given by:
[tex]A = a * b[/tex]
Where:
a, b:they are the sides of the rectangle.
According to the figure we have:
[tex]a = 10\\b = 6[/tex]
Substituting we have:
[tex]A = 10 * 6\\A = 60[/tex]
Thus, the area of the rectangle is [tex]60in ^ 2[/tex]
On the other hand, the area of a triangle is given by:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b is the base and h is the height of the triangle.
According to the figure we have to:
[tex]b = 12-10 = 2\\h = 6[/tex]
Substituting in the formula:
[tex]A = \frac {2 * 6} {2} = \frac {12} {2} = 6[/tex]
Thus, the area of the rectangle is[tex]6in ^ 2[/tex]
Then, the total area of the figure is:
[tex]A_ {T} = 60in ^ 2 +6in ^ 2 = 66 \ in ^ 2[/tex]
Answer:
[tex]66 \ in ^ 2[/tex]
