find the volume of the oblique rectangular prism below. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Find the base - area

The base is a rectangle with length $l = 8$ and width $w = 6$. The area of the base $B$ is given by the formula $B=l\times w$. $B = 8\times6=48$

Step2: Find the height

The slant - height is 8 and the angle between the base and the slant - side is $45^{\circ}$. Since $\sin\theta=\frac{h}{s}$ (where $h$ is the height, $s$ is the slant - height and $\theta$ is the angle between the base and the slant - side), and $\theta = 45^{\circ}$, $\sin45^{\circ}=\frac{\sqrt{2}}{2}$, $s = 8$. So $h=s\sin45^{\circ}=8\times\frac{\sqrt{2}}{2}=4\sqrt{2}\approx5.7$

Step3: Calculate the volume

The volume $V$ of a prism is given by the formula $V = B\times h$. Substitute $B = 48$ and $h\approx5.7$ into the formula. $V=48\times5.7 = 273.6$

Answer:

$273.6$