Answer:
510.4 ft²
Step-by-step explanation:
We have:
two trapezoids with bases 15ft and 7ft and height 5ft.
four rectangles 5ft × 11ft, 15ft × 11ft, 9.4ft × 11ft and 7ft × 11ft.
The formula of an area of a trapezoid:
[tex]A_t=\dfrac{b_1+b_2}{2}\cdot h[/tex]
b₁, b₂ - bases
h - height
Substitute:
[tex]A_t=\dfrac{15+7}{2}\cdot5=\dfrac{22}{2}\cdot5=(11)(5)=55\ ft^2[/tex]
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length
w - width
The dimensions of rectangle l × w
Subtitute:
[tex]A_1=(5)(11)=55\ ft^2\\\\A_2=(15)(11)=165\ ft^2\\\\A_3=(9.4)(11)=103.4\ ft^2\\\\A_4=(7)(11)=77\ ft^2[/tex]
The surface area of the figure:
[tex]S.A.=2A_t+A_1+A_2+A_3+A_4\\\\S.A.=2(55)+55+165+103.4+77=510.4\ ft^2[/text]
