Answer:
[tex]62\ in^2[/tex]
Step-by-step explanation:
we know that
The area of the composite figure is equal to the area of a right triangle plus the area of rectangle
see the attached figure to better understand the problem
step 1
Find the area of the right triangle
we know that
The area of triangle is
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
[tex]b=7-4=3\ in\\h=12-8=4\ in[/tex]
substitute
[tex]A_1=\frac{1}{2}(3)(4)=6\ in^2[/tex]
step 2
Find the area of rectangle
The area of rectangle is equal to
[tex]A=LW[/tex]
where
[tex]L=8\ in\\W=7\ in[/tex]
substitute
[tex]A_2=(8)(7)=56\ in^2[/tex]
step 3
Find the area of the composite figure
Adds the areas
[tex]A=A_1+A_2[/tex]
[tex]A=6+56=62\ in^2[/tex]
