How to find
the surface area and volume of prisms.

This topic is part of the
TCS FREE high school mathematics 'Howto Library',
and will help you to find
the surface area and volume of prisms.
(See the index page
for a list of all available topics in the library.)Â To
make best use of this topic, you need to download the Maths Helper Plus
software. Click
here for instructions. 
Theory:
A 'prism' is a solid figure with a uniform cross section. Here are some
examples of prisms:
Rectangular based prism:

Circular based prism:
(Cylinder)

Triangular based prism:

The surface area of any prism equals the sum of the areas of its faces, which
include the floor, roof and walls. Because the floor and the roof of a prism
have the same shape, the surface area can always be found as follows:
From now on we will call the 'floor'
the 'base'. The height of the prism = 'H'.
The surface area of a
prism = 2 × area of baseÂ +Â perimeter of base × H
The actual formula used to find the surface area will depend on the shape
of the base of the prism.
For example:
Rectangular
based prism
Base
shape: Rectangle, length 'L' and width 'W'
Area
of base: LÂ ×Â W
Perimeter
of base: 2(L+W)
Surface
area = 2LW + 2(L+W)H


Â Â 

Circular
based prism
Base
shape: Circle, radius 'R'
Area
of base: pR²
Perimeter
of base: 2pR
Surface
area = 2pR²
+ 2pRH
Â 

Â Â 

Triangular
based prism
Base
shape: Triangle: base 'b', height 'h', and sides S_{1}, S_{2}
and S_{3}Â
Area
of base: ½b×h
Perimeter
of base: S_{1}+ S_{2} + S_{3}
Surface
area = bh + (S_{1}+
S_{2} + S_{3})H
Â 

The 'Method' section below shows you how to use Maths Helper Plus to
calculate surface areas and volumes of rectangular prisms. Complete working
steps and a labelled diagram and net of the solid are created automatically.
Method:
Â
Step 1 Download
the free support file...
We
have created a Maths Helper Plus document to complement this topic. You can use
it to practice the steps described below, and as a
starting point for solving your own problems.
File
name:Â 'Rectangular prism.mhp'Â Â File size: 20kb
Click here to download the file.
If
you choose 'Open this file from its current location', then Maths Helper Plus should
open the document immediately. If not, try the other option: 'Save this file to disk', then
run Maths Helper Plus and choose the 'Open' command from the 'File' menu. Locate the
saved file and open it. If you do not yet have Maths Helper Plus installed on your
computer, click here
for instructions.

Â
Step 2Â Display
the parameters box
Press the F5 key to display the
parameters box:
Â
'A',
'B' and 'C' are the height, width and depth of the prism.
Click
on the 'A' edit box and enter the height.Â
Similarly,
enter the width and depth values in edit boxes 'B' and 'C'.
Â
Click the
'Update' button to refresh the diagram and calculations.
Â
Step 3Â Adjust
the scale of the labelled diagram
If the labelled diagram does not
display the entire prism and its net, the scale needs to be reduced. In this case, briefly press
the F10 key enough times until the whole diagram is seen.
Â
You can make the diagram bigger by
holding down 'Ctrl' while you press F10.
Â
Still don't understand or
have further questions about this topic ?
Then ask us! Click
here now!

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