Answer:
Part 1) [tex]132\ ft^{2}[/tex]
Part 2) [tex]27\ ft^{2}[/tex]
Step-by-step explanation:
Part 1) we know that
The area of the figure is the area of one trapezoid multiplied by 2
Find the area of one trapezoid
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
we have
[tex]b1=9\ ft[/tex]
[tex]b2=15\ ft[/tex]
[tex]h=11/2=5.5\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(9+15)5.5=66\ ft^{2}[/tex]
Find the area of the figure
[tex]2*66\ ft^{2}=132\ ft^{2}[/tex]
Alternative Method
The area of the figure is equal to the area of a rectangle plus the area of triangle
so
[tex]A=11*9+\frac{1}{2}(11)(15-9)\\ \\A=99+33\\\\A=132\ ft^{2}[/tex]
Part 2) we know that
The area of the hexagon is equal to the area of one triangle multiplied by 6
Find the area of one triangle
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=3\ ft[/tex]
[tex]h=3\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(3*3)=4.5\ ft^{2}[/tex]
[tex]6*4.5\ ft^{2}=27\ ft^{2}[/tex]
