Volume:
With this prism, first separate it into a rectangular prism and a right triangle prism.
First, with the rectangular prism, it would have the units 5 * 5 * 6.3. Then with the right triangle prism, it would take the rest of the remaining space of it, being 3 * 5 * 6.3
The equation for the volume of a rectangular prism is L*W*H and the equation for the volume of a right triangle prism is (L*W*H) / 2.
With this, plug the numbers in for both prisms to get the volume of each of them:
Rectangular prism Volume
5*5*6.3
157.5
Right triangle prism Volume
(3*5*6.3) / 2
94.5 / 2
47.25
Lastly, combine these two values to get the total volume:
157.5 + 47.25 = 204.75 (Round Up) -->
204.8 cm^3 = Total Volume
Surface Area:
Next, with the surface area of the prism. For this, lets combine all of the faces of the prism then add them all up.
First, lets do the bottom of the prism, or the base. It uses the lengths 8 cm and 6.3 cm. Lets do L * W to get the area of this face:
8 * 6.3 = 50.4
Next, lets do the slant side of it, which has the lengths 5.8 and 6.3.
5.8 * 6.3 = 36.54
Then, the top side with the lengths 5cm and 6.3 cm.
5.3 * 6.3 = 33.39
After that, the left side face that opposite to the slantly one:
5 * 6.3 = 31.5
Saving the most tedious part of it for last, the right trapezoids. Luckily, there is an equation for this:
1/2 x (Sum of parallel sides) x (perpendicular distance between the parallel sides).
So, within each of these right trapezoids, there's the parallel sides of 5 and 8. There's also a perpendicular side of 5cm. With this, we can plug this into the equation to solve for this part:
1/2 x (5+8) * (5)
1/2 x (13) * (5)
1/2 x (65)
32.5
Since there's two of them, times this by 2:
32.5 * 2 ---> 65.
Now, with the area of all of the faces, these can be added up for the total surface area:
50.4 + 36.54 + 33.39 + 31.5 + 65 ---> 216.83 (Round Down)-->
216.8 cm^2 = Total Surface Area
