Surface Area of a Cuboid - Mathematics

SURFACE AREA OF A CUBOID

Have you looked at a bundle of many sheets of paper? How does it look? This is how a bundle of papers would look like. That makes up a Cuboid.
Let us see how much of brown paper would you need if you want to cover this Cuboid. First we would need a rectangular piece to cover the bottom part of the bundle. Then we would need two long rectangular pieces to cover the two side ends.
Now to cover the front and the back ends, we would need two more rectangular pieces of a different size. This figure when opened out would look like this and finally to cover the top of the bundle, we would require another rectangular piece exactly like the one at bottom.
Attach this rectangular piece on the right side. We know has used six rectangular pieces to cover the complete outer surface of the Cuboid. This shows us that the outer surface of the Cuboid is made of six rectangles in fact the rectangular regions called the faces of the Cuboid whose areas can be found by multiplying length by breadth for each of them separately and then adding the six areas together.
If we take the length of the Cuboid as l, breadth as b and the height as h, then the sum of the areas of the six rectangles is
= Area of rectangle 1 (l*h) + Area of rectangle 2 (l*b) + Area of rectangle 3 (l*h) + Area of rectangle 4 (l*b) + Area of rectangle 5 (b*h) + Area of rectangle 6 (b*h)
= 2(l*b) + 2(b*h) +2(l*h)
= 2(lb + bh + hl)
This gives us the surface area of a Cuboid which is = 2(lb + bh + hl) where l, b and h are respectively the three edges of a Cuboid.