Answer:
Approximately 201 squared inches.
Step-by-step explanation:
So, the composite figure is made up of a square and a semi-circle. The square has side lengths of 12 and the semi-circle has a radius of 6.
The total area of the figure would be the area of the square plus the area of the semi-circle. Thus, find the area of each individual figure.
Square:
The area of a square is given by:
[tex]A=l^2[/tex]
Where l is the side length.
Substitute 12 for l:
[tex]A=(12)^2\\A=144\text{ in}^2[/tex]
So the square is 144 square inches.
Semi-circle:
The area of a semi-circle is given by:
[tex]A=\frac{1}{2}\pi r^2[/tex]
Substitute 6 for r and 3.14 for π:
[tex]A=\frac{1}{2}(3.14)(6)^2\\ A=56.52[/tex]
Therefore, the total area is:
[tex]TA=144+56.52\\TA=200.52\text{ in}^2\approx201\text{ in}^2[/tex]
