Considering that the logo is composed by a semi-circle, a square and a right triangle, it's area is of 143.47 square inches.
The area of a semi-circle of radius r is given by:
[tex]A = 0.5\pi r^2[/tex]
In this problem, the radius is of r = 7 in, hence it's area in square inches is of:
[tex]A_{sc} = 0.5\pi \times 7^2 = 76.97[/tex]
The area of a square of side l is given by:
[tex]A = l^2[/tex]
In this problem, we have that l = 7 in, hence it's area in square inches is of:
[tex]A_{sq} = 7^2 = 49[/tex]
The area of a right triangle of sides a and b is given by:
[tex]A = \frac{ab}{2}[/tex]
In this problem, we have that a = 5 in, b = 7 in, hence it's area in square inches is of:
[tex]A_{rt} = \frac{5 \times 7}{2} = 17.5[/tex]
It is given by the sum of the areas of each figure, hence:
[tex]A = A_{sc} + A_{sq} + A_{rt} = 76.97 + 49 + 17.5 = 143.47[/tex]
It's area is of 143.47 square inches.
More can be learned about the area of a figure at https://brainly.com/question/11423300