In order to find the surface area we need to calculate the area of each face
We have two faces with his shape
[tex]A_1=(2\cdot9)+(3\cdot2)=24yd^2[/tex]then we have rectangles in the other faces the formula of the area of a rectangle is l times w where l is the length and w is the width
where A2 is the bottom face and A7 is the lateral face that we can't see in the image but we know they exist
[tex]A_2=9\cdot12=108yd^2[/tex][tex]A_3=12\cdot2=24yd^2[/tex][tex]A_4=7\cdot12=84yd^2[/tex][tex]A_5=3\cdot12=36yd^2[/tex][tex]A_6=2\cdot12=24yd^2[/tex][tex]A_7=5\cdot12=60yd^2_{}[/tex]In order to calculate the surface area we sum all the areas we found remember we have 2 faces with the A1
[tex]\begin{gathered} SA=2A_1+A_2+A_3+A_4+A_5+A_6+A_7_{} \\ \end{gathered}[/tex]we substitute the values
[tex]SA=2(24)+108+24+84+3624+60=384yd^2[/tex]The surface area of the figure is 384 yd^2
Then for the volume, we have the next formula
[tex]V=A_1\cdot w[/tex]where
A1=24yd^2
w=12yd
we substitute the values
[tex]V=24\cdot12=288yd^3[/tex]the volume of the figure is 288yd^3
