Surface area

[mumssie]

Can anyone tell me how to calculate the surface area of a cuboid when laid flat. Obviously not the same as normally finding s/a.. Id really appreciate it if somebody would let me know. Many thanks

[JRM]

Do you mean when it is laid flat as a net?

[Okanagan]

You have 3 measurements: length(L), width(W) and height(H).
You will have 2 each of:
L * W
L * H
W * H

Total surface area
2 * (L*(W+H) + (W*H))

[leanmeamum]

If your child finds it hard to visualize a net then they can just work out the area of 3 faces visible to them (this works for cubes and cuboids) and multiply each by 2 and then add them together.

cube - surface area = area of 1 face X 6

cuboid -
surface area = 2(L x H) + 2(L x W) + 2(H x W)

A cube is just 6 squares stuck together and a cuboid is 6 rectangles stuck together - when the child understands this, the calculation becomes really easy. Even if they forget the formula, they can quickly work out the answer.

[mystery]

Mummsie, didn't really understand your question. How can the same cuboid have two different surface areas?

[JRM]

Mummsie, didn't really understand your question. How can the same cuboid have two different surface areas?

That's what I was trying to work out.

Unless you have to work out the 'visible' surface area? I suppose in that case you would just not include the rectangle on the bottom, and then it would matter which end it was standing on.

[Okanagan]

But visible surface area would be what you could actually see from one particular point at any one time - so just 3 faces maximum - maybe only 1, depending upon your perspective.

I took it to mean the "area of the net laid flat" - which is equal to the surface area of the cuboid.

[JRM]

Yes, I was just guessing. Don't anyone take my comment as an answer.

[leanmeamum]

But visible surface area would be what you could actually see from one particular point at any one time - so just 3 faces maximum - maybe only 1, depending upon your perspective.

I took it to mean the "area of the net laid flat" - which is equal to the surface area of the cuboid.

It is the area of the net - I was just trying to explain the theory behind the calculation - assuming 3 faces are visible for a 3D shape.

Your calculation is correct but I was trying to break down the logic if the child can't see it in their head as some children find it hard to visualize 3D objects without having a model to look at.

[leanmeamum]

Mummsie, didn't really understand your question. How can the same cuboid have two different surface areas?

It would be the same as the measurements remain the same whether it is 3D or laid out flat as a net