Final answer:
To find the volume of the prism, we need to calculate the cross-sectional area of the base and multiply it by the height. The base is a triangle in the xy-plane bounded by the x-axis and the lines y=x and x=1. The top of the prism lies in the plane z = 3 - x - y.
Step-by-step explanation:
To find the volume of the prism, we need to calculate the cross-sectional area of the base and multiply it by the height. The base is a triangle in the xy-plane bounded by the x-axis and the lines y=x and x=1. The top of the prism lies in the plane z = 3 - x - y.
To find the cross-sectional area, we can find the length of the base of the triangle, which is the difference between the x-coordinates of the two vertices at (1, 1) and (1, 0). This length is 1 - 1 = 0. Since the triangle is right-angled, the height of the triangle is the y-coordinate of the vertex at (1, 1), which is 1.
Therefore, the cross-sectional area of the base is 0.5 * 0 * 1 = 0. To find the volume of the prism, we multiply the cross-sectional area by the height, which is given as z = 3 - x - y. Substituting 0 for x and 1 for y, we have z = 3 - 0 - 1 = 2.
Therefore, the volume of the prism is 0 * 2 = 0.