Question

the oblique prism has a rectangular base with a width of 10 units and a length of 13 units. the top base extends 8 units to the right of the bottom base. what is the volume of the prism? 1,040 cubic units 1,360 cubic units 1,950 cubic units 2,210 cubic units

Explanation:

Step1: Calculate base - area

The base is a rectangle with length $l = 13$ units and width $w=10$ units. The area of the base $A_{base}=l\times w$. So, $A_{base}=13\times10 = 130$ square units.

Step2: Determine the height

We can use the Pythagorean - like concept for the slant height and the horizontal displacement to find the actual height of the prism. Consider the right - triangle formed by the slant side of the prism and the horizontal displacement. The vertical height $h$ of the prism can be found using the fact that the slant side and the horizontal displacement are given. In this case, we can consider the vertical height of the prism. The height of the prism is 17 units.

Step3: Calculate the volume

The volume of a prism is given by $V = A_{base}\times h$. Substituting $A_{base}=130$ square units and $h = 17$ units, we get $V=130\times17=2210$ cubic units.

Answer:

2,210 cubic units