For this case we have that the figure is made up of two rectangles and a quarter circle.
By definition we have to:
The area of a rectangle is given by:
[tex]A = a * b[/tex]
Where:
a and b: Are the sides of the rectangle
The area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle
So:
Rectangle 1:
[tex]A_ {1} = 16 * 6 = 96 \ cm ^ 2[/tex]
Rectangle 2:
[tex]A_ {2} = 11 * 5 = 55 \ cm ^ 2[/tex]
A quarter of a circle:
[tex]A = \frac {\pi * (4) ^ 2} {4} = \frac {3.14 * 16} {4} = 12.56 \ cm ^ 2[/tex]
Thus, the total area is:
[tex]A_{t} = A_{1} + A_{2} + A_{3} = (96 + 55 + 12.56) \ cm ^ 2 = 163.56 \ cm ^ 2[/tex]
Answer:
The area of the figure is:[tex]163.56 \ cm ^ 2[/tex]
