First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
![240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2](https://tex.z-dn.net/?f=240in%5E2%5Ccdot%5Cfrac%7B%281yd%29%5E2%7D%7B%2836in%29%5E2%7D%3D0.185yd%5E2)
Now, to find the volume convert 30 in to yards:
![30in\cdot\frac{1yd}{36in}=0.83yd](https://tex.z-dn.net/?f=30in%5Ccdot%5Cfrac%7B1yd%7D%7B36in%7D%3D0.83yd)
Finally, multiply the previous result by the area of the figure: