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 cm^{2}.

**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 cm*^{2}

**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 cm*^{2}

**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 cm^{2}

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