Answer:
Part a) The area of the figure is [tex]31\ ft^2[/tex]
Part b) The area of the figure is [tex]46\ ft^2[/tex]
Step-by-step explanation:
Part a) we know that
The area of the figure is equal to the area of rectangle plus the area of trapezoid
step 1
The area of rectangle is
[tex]A_1=(b)(h)[/tex]
we have
[tex]b=8\ ft\\h=2\ ft[/tex]
substitute the given values
[tex]A_1=(8)(2)=16\ ft^2[/tex]
step 2
The area of trapezoid is
[tex]A=\frac{1}{2}(b_1+b_2)(h)[/tex]
we have
[tex]b_1=4\ ft\\b_2=8-(1+1)=6\ ft\\h=3\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(4+6)(3)[/tex]
[tex]A_2=15\ ft^2[/tex]
step 3
Find the area of the figure
[tex]A=A_1+A_2[/tex]
substitute
[tex]A=16+15=31\ ft^2[/tex]
Part b) we know that
The area of the figure is equal to the area of rectangle plus the area of two triangles
step 1
The area of rectangle is
[tex]A_1=(b)(h)[/tex]
substitute the given values
[tex]A_1=(5)(6)=30\ ft^2[/tex]
step 2
The area of triangle at the top is
[tex]A_2=\frac{1}{2}(b)(h)[/tex]
we have
[tex]b=4\ ft\\h=6\ ft[/tex]
substitute
[tex]A_2=\frac{1}{2}(4)(6)[/tex]
[tex]A_2=12\ ft^2[/tex]
step 3
The area of triangle at right is
[tex]A_3=\frac{1}{2}(b)(h)[/tex]
we have
[tex]b=4\ ft\\h=2\ ft[/tex]
substitute
[tex]A_3=\frac{1}{2}(4)(2)[/tex]
[tex]A_3=4\ ft^2[/tex]
step 4
Find the area of the figure
[tex]A=A_1+A_2+A_3[/tex]
substitute
[tex]A=30+12+4=46\ ft^2[/tex]
