the oblique prism has a rectangular base with a width of 10 units and a length of 13 units. the top base…

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

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

Answer

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 $A$ of a rectangle is given by $A = l\times w$. So, $A=13\times10 = 130$ square units.

Step2: Determine the height

The height $h$ of the prism is the perpendicular distance between the bases. Using the Pythagorean - like concept for the right - triangle formed by the slant height and the offset of the bases. The height $h$ of the prism can be found from the right - triangle with hypotenuse 17 and one side 8. By the Pythagorean theorem $h=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15$ units.

Step3: Calculate the volume

The volume $V$ of a prism is given by $V=A\times h$. Substituting $A = 130$ and $h = 15$ into the formula, we get $V=130\times15=1950$ cubic units.

Answer:

1,950 cubic units