i need to know how to work out the volum and surface area of this shape, if you know how to please post:

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- Jun 24th 2009, 09:19 AMandyboy179volume and surface area
i need to know how to work out the volum and surface area of this shape, if you know how to please post:

Attachment 11980 - Jun 24th 2009, 09:21 AMUnenlightened
- Jun 24th 2009, 09:34 AMmasters
Hi andyboy179,

This shape would appear to be a rectangular prism.

The lateral area (area of every side except top and bottom) is given by the formula:

**LA = ph**(perimeter of the base multiplied by the height)

The surface area is then found by adding the LA to the areas of the Bases (top and bottom).

**SA = LA + 2B**

In your figure:

LA = 18 times 3 = 54 square cm

SA = 54 + 2(14) = 82 square cm

The volume of a right rectangular prism is given by the formula:

**V = LWH**(length times width times height)

In your case,

V = 7 X 2 X 3 = 42 cubic cm. - Jun 24th 2009, 09:36 AMandyboy179
- Jun 24th 2009, 09:49 AMandyboy179
im still confused, right could we do the volume first, how would i do that?

- Jun 24th 2009, 09:51 AMe^(i*pi)
- Jun 24th 2009, 09:52 AMUnenlightened
Fair enough.

Well, on the offchance you can't understand masters' explanation; the easiest way to get the area is just to say: Total surface area = Sum of the areas of each face.

So you've six faces, all rectangles. The area of a rectangle is obtained by just multiplying the two sides.

So, say, the face at the top is 7x2 = 14.

And the face at the bottom will be the same = 14.

The face in front is 7x3=21

As is the one at the back = 21.

The other face you can see is 3x2 = 6.

And the corresponding one that you can't see =6 also.

So the sum of the four squares is 14+14+21+21+6+6 = 82. - Jun 24th 2009, 09:55 AMandyboy179
- Jun 24th 2009, 09:58 AMe^(i*pi)
- Jun 24th 2009, 09:58 AMUnenlightened
- Jun 24th 2009, 10:00 AMandyboy179
sorry thats what i meant, silly me. now the surface area, i have no idea on how to do this could u help please?

- Jun 24th 2009, 10:13 AMmasters
Whatever the rectangular prism is sitting on, we'll call that the base. In your case, the base is 7 by 2. The top is the same shape as the base, so it is also 7 by 2.

The Surface Area is found by adding the areas of all the faces or more simply, if the base is "**l**" by "**w**" and the height is "**h**", then the surface area is given by:

**SA = 2(lw + hl + hw)**

Another method I already gave you in my earlier post. - Jun 24th 2009, 10:40 AMHallsofIvy
The surface of the figure consists of 6 rectangles. The area of a rectangle is "height times width". Calculate the area of each rectangle and add them (opposite rectangles will have the same area so you really only need to find 3 areas).