Answer
143 yd²
Step-by-step explanation
The surface area of the shape is composed of 2 trapezoids with bases of 3 and 7 yd and a height of 3.5 yd, 2 rectangles with dimensions 6x4 yd, 1 rectangle with dimensions 6x7 yd, and 1 rectangle with dimensions 6x3 yd.
The area of the trapezoids is calculated as follows:
[tex]\begin{gathered} A_{trapezoid}=\frac{base_1+base_2}{2}\cdot height \\ A_1=\frac{3+7}{2}\cdot3.5 \\ A_1=5\cdot3.5 \\ A_1=17.5\text{ yd}^2 \end{gathered}[/tex]
The area of the rectangles is calculated as follows:
[tex]\begin{gathered} A_{rectangle}=lenght\cdot width \\ A_2=6\cdot4=24\text{ yd}^2 \\ A_3=6\cdot7=42\text{ yd}^2 \\ A_4=6\cdot3=18\text{ yd}^2 \end{gathered}[/tex]
Finally, the surface area is:
[tex]\begin{gathered} SA=2A_1+2A_2+A_3+A_4 \\ SA=2\cdot17.5+2\cdot24+42+18 \\ SA=35+48+42+18 \\ SA=143\text{ yd}^2 \end{gathered}[/tex]
