Answer:
14.5 [tex]in^2[/tex]
Step-by-step explanation:
Subtraction of Areas
To calculate the area of certain shapes is necessary to compute two areas and have them subtracted.
The required area (in the colored background) is the area of the triangle minus the area of the rectangle.
[tex]\displaystyle A=\frac{bh}{2}-b'.h'[/tex]
We need to know the base of the triangle, which is the sum of 5 inches+4 inches= 9 inches.
We can also calculate the height of the triangle as the sum of 2+5= 7 inches
The rectangle in the bottom right corner has a base of 4 in and a height of 2 in, thus
[tex]\displaystyle A=\frac{9\cdot 5}{2}-4\cdot 2=22.5-8=14.5\ in^2[/tex]
[tex]A=14.5\ in^2[/tex]
