What is Cuboid?
A cuboid is a three dimensional figure bounded by six rectangular planes,having different magnitude of length, width and height. If you look around and you can see a box, a brick or anything in the shape of a rectangular could be cuboid.
It has six rectangular sides, called faces, and each face of a cuboid is a rectangle, and all of a its corners are 90-degree angle
Surface Area of Cuboid
A common mistake is to confuse area with the volume of cuboids, which are totally different aspect. The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces.
Formula for Surface Area of Cuboid:
Before going into the concept of area, let us denote the dimensions of a cuboid, which are,
Length, Width and Height which are represented by l, w, h respectively.
The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:
TSA = 2 (lw + wh + lh)
The above formula gives the total surface area of a cuboid having all the six sides. However, there is one more term which is commonly used for measurement of area of a cuboid, which is the lateral surface area of a cuboid (LSA).
The lateral surface area of a cuboid is the sum of 4 planes of a rectangle, leaving the top (upper) and the base (lower) a. Mathematically, LSA is given as:
LSA = 2 (lh + wh) = 2 h (l + w)
Example of Surface Area of Cuboid
Example 1: Given below is a cuboid having it’s dimension given as l=8 cm, w=6 cm and h=5 cm, find the TSA of a cuboid.
h = 5 cm
w = 6 cm
l = 8 cm
Using the formula: TSA = 2 (lw + wh + hl)
=\(2(8 \times 6 + 6 \times 5 + 5 \times 8)\)
= \(2(48 + 30 + 40)\)
So, the total surface area of this cuboid is 236 cm2.
Example 2: The dimensions of a cuboid are given as follows:
Length = 4.8 cm
Width = 3.4 cm
Height = 7.2 cm.
Find the Total and the Lateral Surface area.
The total surface area is given as
TSA = 2 (lw + wh + hl)
=\(2(4.8 \times 3.4 + 3.4 \times 7.2 + 7.2 \times 4.8)\)
= \(2(34.56+ 24.48 + 16.32)\)
= 2(75.36) cm²
TSA = 150.72 cm
Also, the lateral surface area = 2 h (l + w)
= 2 \(\times\)7.2 (4.8 + 3.4)
= 14.4 (8.2)
= 53.76 cm²