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### Volume of a Rectangular Solid

```
Date: 4/4/96 at 8:15:12
From: Elena Viola
Subject: (no subject)

How do you calculate the lateral area, total area, and volume of a
rectangular solid with the following dimensions:

Length 4 decimeters
Width  3 decimeters
Height 2 decimeters

Thanks
```

```
Date: 4/4/96 at 14:25:55
From: Doctor Ethan
Subject: Re: Rectangular Solids

Hey Elena,

Well first let's recall a few definitions.

The total area is the sum of the area of all the faces.

The lateral area is the total area minus the area of the top
and bottom - or you could say the the lateral area is
the sum of the areas of the sides.

The volume is the area of the base times the height.

Here, since the height is given as 2, the side with lengths 3 and 4
is considered to be the base.

So the area of the base is 3*4 = 12, and that will also be the area of
the top.  To find the volume we just multiply this by the height,
which is 2.

So the volume is 24.

Now let's find the total area. That will be
2 sides of area 3*4
2 sides of area 2*3
2 sides of area 2*4

which is 12 + 12 + 6 + 6 + 8 + 8 = 52.

So 52 is the total area.

To find the lateral area just subtract the area of the top and
bottom: 52 - 12 - 12 = 28.

Remember that the lateral area would be different if you had
labeled the values differently.

Hope that helps.

-Doctor Ethan,  The Math Forum

```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
Middle School Geometry
Middle School Higher-Dimensional Geometry

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