Answer:
59 in2
Step-by-step explanation:
we know that
The area of the polygon is equal to the area of rectangle plus the area of two triangles
so
Find the area of rectangle
[tex]A_1=LW[/tex]
we have
[tex]L=7\ in\\W=4\ in[/tex]
substitute
[tex]A_1=(7)(4)=28\ in^2[/tex]
Find the area of triangle with height of 6 in
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=7\ in\\h=6\ in[/tex]
substitute
[tex]A_2=\frac{1}{2}(7)(6)=21\ in^2[/tex]
Find the area of triangle with height of 5 in
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=4\ in\\h=5\ in[/tex]
substitute
[tex]A_3=\frac{1}{2}(4)(5)=10\ in^2[/tex]
The total area is
[tex]A=A_1+A_2+A_3=28+21+10=59\ in^2[/tex]
