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How to find the surface area and volume of prisms.

 This topic is part of the TCS FREE high school mathematics 'How-to 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.) 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 base  +  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: L  × W Perimeter of base: 2(L+W) Surface area = 2LW + 2(L+W)H Circular based prism Base shape: Circle, radius 'R' Area of base: pR² Perimeter of base: 2pR Surface area = 2pR² + 2pRH Triangular based prism Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3  Area of base: ½b×h Perimeter of base: S1+ S2 + S3 Surface area = bh + (S1+ S2 + S3)H

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:

 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:  'Rectangular prism.mhp'   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.

#### Step 2  Display the parameters box

Press the F5 key to display the parameters box:

'A', 'B' and 'C' are the height, width and depth of the prism.

Click on the 'A' edit box and enter the height.

Similarly, enter the width and depth values in edit boxes 'B' and 'C'.

Click the 'Update' button to refresh the diagram and calculations.

#### Step 3  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.

You can make the diagram bigger by holding down 'Ctrl' while you press F10.

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