What is a lateral face ?
Any face of a cuboid can be taken as its base, the 4 faces that meet the base are called the lateral face. ( What are Faces in Cuboid ? )
What is a lateral surface area or curved surface of cuboid ?
Suppose we have a cuboid shape room like as below
so lateral surface area of room includes - length, breadth and height of room (and we do not include ceiling and floor)
so the formula to find the Lateral surface area of cuboid = 2H [L + B]
How formula of lateral surface area of cuboid is obtained
Observe the following diagram of cuboid:
Red lines represent length of cuboid (L)
Green lines represent breadth of cuboid (B)
Blue lines represent height of cuboid (H)
Lateral surface includes four faces of the cuboid i.e. left side face, right side face, front face and back face (as shown in following four pictures):
Lateral Surface Area of Cuboid = Area Left side face + Area of Right side face + Area of Front Face + Area of Back Face ..... (Statement 1)
Since all faces are in the shape of rectangle, so to find area of faces; apply formula of area of rectangle and we get:
Area of Left Face = Length X breadth
As shown in the diagram, length = height, so we get:
Area of Left Face = height X breadth = H X B ... (Statement 2)
Similarly, Area of Right Side Face = H X B ... (Statement 3)
Area of Front Face = L X H ... (Statement 4)
Area of Back face = L X H ... (Statement 5)
Now put the values of all faces from statement 2, 3, 4 & 5 and put them into statement 1. And we get:
Lateral Surface Area of Cuboid = (H X B) + (H X B) + (L X H) + (L X H)
Combining terms and we get:
LSA of cuboid = 2(H X B) + 2(L X H)
Open brackets and we get:
LSA of cuboid = 2H X 2B + 2L X 2H
Taking common terms and we get:
LSA of cuboid = 2H (L X B)
Hence, in this way Lateral Surface Area of Cuboid is obtained:
Lateral Surface Area of Cuboid = 2H (L X B)
Note: Lateral surface area of cuboid is always in square units. e.g. cm2, m2, mm2 etc
Let's try out some examples
Example 1 : The length, breadth and height of cuboid shape room are 5m, 4m and 3m respectively. Find the lateral surface area of room
Solution : The given things are
Length = 5m
Breadth = 4m
Height = 3m
Lateral surface area = 2H [L + B]
L.S.A. of cuboid (room) = 2 X 3 [5 + 4]
L.S.A. of cuboid (room) = 6 [9]
L.S.A. of cuboid (room) = 6 X 9
L.S.A. of cuboid (room) = 54m2
Example 2 : The length, breadth and height of cuboid shape hall are 15m, 20m and 25m respectively. Find the lateral surface area of hall
Solution : The given things are
Length = 15m
Breadth = 20m
Height = 25m
Lateral surface area = 2H [L + B]
L.S.A. of cuboid (hall) = 2 X 25 [15 + 20]
L.S.A. of cuboid (hall) = 50 [35]
L.S.A. of cuboid (hall) = 50 X 35
L.S.A. of cuboid (hall) = 1750m2
Study More Solved Questions / Examples
The length, breadth and height of cuboid shape room are mentioned below. Find the lateral surface area of room ?
A) 83 cm, 78 cm and 58 cm
B) 92 cm, 99 cm and 47 cm
C) 36 cm, 78 cm and 43 cm
|
The length, breadth and height of cuboid shape room are mentioned below. Find the lateral surface area of room ?
A) 28 meter, 15 meter and 15 meter
B) 9 meter, 18 meter and 7 meter
C) 18 meter, 8 meter and 19 meter
D) 19 meter, 30 meter and 18 meter
E) 20 meter, 27 meter and 16 meter
F) 7 meter, 5 meter and 19 meter
G) 5 meter, 9 meter and 19 meter
H) 6 meter, 28 meter and 12 meter
|
| | |
