find the lateral area, the total & the volume of the retangular solids w/ the given dimensions.L=6W=5H=3?

Answer 1

The lateral area of any right prism is the perimeter of the base times the height. If you remember it this way, it's much easier - it accounts for the base to be of any shape - rectangles, triangles, pentagons, and even circles (in which case you'd have a cylinder, which is essentially the same as a right prism).

In your problem, you have the length, width, and height:

L = 3

6W = 3
W = 1/2

5H = 3
H = 3/5

So we can find the lateral area first. The perimeter of the base is 3 + 1/2 + 3 + 1/2 = 7. The height is 3/5, so LA = 21/5.

The total area of any right prism is the lateral area plus twice the area of a base. Again, this works for any right prisms, including cylinders. In your problem, the area of the base is 3 * 1/2, or 3/2. You need two of these plus the LA, so the total area is then 21/5 + 2(3/5) = 36/5.

The volume of the prism is the area of the base times the height. The area of the base is 3/2 (we found that already), and the height is 3/5. So the volume is then 3/2* 3/5 = 9/10.