210 MATHEMATICS
This shows us that the outer surface of a cuboid is made up of six rectangles (in
fact, 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.
Now, if we take the length of the cuboid as l, breadth as b and the height as h, then
the figure with these dimensions would be like the shape you see in Fig. 13.2(f).
So, 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:Surface Area of a Cuboid = 2(lb + bh + hl)where l, b and h are respectively the three edges of the cuboid.
Note : The unit of area is taken as the square unit, because we measure the magnitude
of a region by filling it with squares of side of unit length.
For example, if we have a cuboid whose length, breadth and height are 15 cm,
10 cm and 20 cm respectively, then its surface area would be:
2[(15 × 10) + (10 × 20) + (20 × 15)] cm^2
= 2(150 + 200 + 300) cm^2
= 2 × 650 cm^2
= 1300 cm^2