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Surface Area of a Cuboid

The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is given by:

TSA = 2 (lw + wh + hl)



Remember the surface area is the total area of all the faces of a 3D shape.
The lateral surface area of a cuboid is given by:

LSA = 2 (lh + wh) = 2 h (l + w)



Example 1: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.
TSA = 2 (lw + wh + hl)
TSA = 2 (8*6 + 6*5 + 5*8)
TSA = 2 (48 + 30 + 40)
TSA = 236
So, the total surface area of this cuboid is 236 cm2.


Example 2: Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm and 7.2 cm.
Solution:
Area of Face 1:
4.8 × 7.2 = 34.56 cm²
Area of Face 2: 3.4 × 7.2 = 24.48 cm²
Area of Face 3: 4.8 × 3.4 = 16.32 cm²

Adding the area of these 3 faces gives 75.36 cm², since each face is duplicated on the opposite side, the total surface area of the cuboid will be:
TSA = 2 (75.36) = 150.72 cm²


Example 3: The length, width and height of a cuboid are 10cm, 8cm and 7cm respectively. Find the lateral surface area of a cuboid.
Solution:
Lateral surface area of cuboid is given by:

LSA = 2h(l+w)
where,
l = length = 10 cm
w = width = 8 cm
h = height = 7 cm

Insert these values into the formula we will get:

LSA = 2 ×7(10 + 8)
LSA = 14 × 18
LSA = 252 cm2


Example 4: The length, breadth and height of a cuboid are 16cm, 14cm and 10cm respectively. Find the total surface area of the cuboid.
Solution:
The total surface area of a cuboid is given by:

TSA = 2 (l*b + b*h + h*l)


Given that:
l = 16cm
b = 14cm
h = 10cm

Substituting the values in the equation we will get
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(224 + 140 + 160)
TSA = 2 * 524
TSA = 1048 cm2


Example 5: Given a cereal box whose length is 20 cm, height is 30 cm and width is 8 cm. Find the surface area of the box.
Solution:
To find the surface are of the box we need to find the area of each rectangular face and add them all up.
The area of the front face is:
20 x 30 = 600 cm2.
The area of the top face is: 20 x 8 = 160 cm2.
The area of the side face is: 8 x 30 = 240 cm2.

Now add these values together we will get: 600 + 160 + 240 = 1000 cm2.


And the total surface area is therefore 1000 x 2 = 2000 cm2.

Example 6: Find the surface area of a cuboid whose sides are 3cm by 6cm by 10cm.
Solution:
Surface area of the cuboid is given by:

TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(3 x 6 + 6 x 10 + 3 x 10)
TSA = 2(18 + 60 + 30)
TSA = 216 cm2


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