So we have:
To find the area of the entire figure we can simply find the areas of each individual subfigure.
For rectangle A we have that its area is given by:
[tex]S_A=5in\cdot10in=50in^2[/tex]For rectangle B:
[tex]S_B=7in\cdot x[/tex]Where side x is given by:
[tex]\begin{gathered} x+6in=10in \\ x=10in-6in=4in \end{gathered}[/tex]Then the surface of rectangle B is:
[tex]S_B=7in\cdot4in=28in^2[/tex]C is a triangle, the area of a triangle is given by its base (y) times its height (x) divided by two:
[tex]S_C=\frac{x\cdot y}{2}=\frac{4in\cdot y}{2}[/tex]We need to find y using the length of the base of the total figure:
[tex]\begin{gathered} 15in=7in+5in+y=12in+y \\ y=15in-12in=3in \end{gathered}[/tex]Now that we found y we can find the area of the triangle:
[tex]S_C=\frac{4in\cdot y}{2}=\frac{4in\cdot3in}{2}=6in^2[/tex]The total area is then:
[tex]S_A+S_B+S_C=50in^2+28in^2+6in^2=84in^2[/tex]So the total area is 84 square inches.
