Welp, here we go. First we want to calculate the volume of the rectangular prism and subtract it from the triangular prism.
Volume of Rectangular Prism:
Let V1 be the volume of the rectangular prism.
V1 = base * height * length.
The base and the height are both 1.7, but the length is the same length of the triangular prism, which is 4. Thus:
V1 = 1.7 X 1.7 X 4
V1 = 11.56 cubic units
Volume of Triangular Prism:
Let V2 be the volume of the triangular prism:
V2 = (base X height X length) / 2
V2 = (5 X 5.7 X 4)/2
V2 = 57 cubic units.
Now we find the total volume. Let Vt be the total volume. The total volume is the shaded minus the unshaded. Thus:
Vt = V2 - V1
Vt = 57 cubic units - 11.56 cubic units
Vt = 45. 44 cubic units
Therefore the volume of the shaded region is 45.44 cubic units.