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Surface Area of Cuboid Formula | Calculate LSA, CSA, TSA of Cuboid, Examples

Surface Area Of Cuboid

The Surface Area Of Cuboid can be calculated by the sum of the areas of all 6 faces of the cuboid. A cuboid is a closed 3-dimensional geometrical structure bounded by six rectangular plane regions.

Cuboid is made of six rectangles and each rectangle is known as face. Students can also get the LSA, CSA, TSA of Cuboid with examples from this page which is well created by the team members of recruitmentresult.com.

Students can learn all the formulas of Cuboid by going through beneath segment of this page. Aspirants are advised to do practice more from these solved examples furnished here to learn Surface Area of Cuboid and other formula on finger tip.

Surface Area Of Cuboid

What is Cuboid?

Cuboid is a closed 3-dimensional geometrical figure made from 6 rectangular plane regions. For example, a matchbox, a tea packet, a chalk box, a dice, a book etc, all these objects have a similar shape. In fact, all these objects are made of six rectangular planes. The shape of these objects is a cuboid.

cuboid

Faces

Cuboid is made up of six rectangles and each of the rectangle is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6-faces of cuboid. The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces.

Any two faces other than the opposite faces are called adjacent faces.

Here, adjacent faces are ABCD, ABFE and ABCD, AEHD.

Know How to Calculate: Surface Area of Cube Formula

Base and Lateral Faces

Any face of a cuboid may be called as the base of the cuboid. The four faces which meet the base are called the lateral faces of the cuboid.

In Figure (1) above, EFGH represents the base of a cuboid.

Edges

The edge of the cuboid is a line segment between any two adjacent vertices.

There are 12 edges, they are AB,AD,AE,HD,HE,HG,GF,GC,FE,FB,EF and CD and the opposite sides of a rectangle are equal.

Hence, AB=CD=GH=EF,AE=DH=BF=CG and EH=FG=AD=BC.

Vertex

The point of intersection of the 3 edges of a cuboid is called vertex of a cuboid.

A cuboid has 8 vertices A,B,C,D,E,F, G and H represents vertices of cuboid in fig 1.

By observation, the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length so there are three distinct groups and the groups are named as length, breadth and height.

Get Here: Area of Semicircle Formula

Surface Area Of A Cuboid

Surface Area Of A Cuboid

The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.

Consider a cuboid having length is ‘l’ cm, breadth is ‘b’ cm and height ‘h’ cm.

Area of face EFGH = Area of Face ABCD = (l×b)cm2

Area of face BFGC = Area of face AEHD = (b×h)cm2

Area of face DHGC = Area of face ABFE = (l×h)cm2

Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces

= 2(l × b) + 2(b × h) +2(l × h)

= 2(lb + bh +lh)

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Lateral Surface Area/ Curved Surface Area Of Cuboid

The sum of surface areas of all sides except top and bottom face of solid is defined as lateral surface area of a solid.

Consider a Cuboid of length,breadth and height to be l, b and h respectively.

Lateral Surface Area Curved Surface Area Of Cuboid

Lateral surface area of the cuboid

= Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH

=2(b × h) + 2(l × h)

=2h(l + b)

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Solved Examples

Question 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

Question 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

Get Formula Of Total, Curved, Lateral Surface Area: Surface Area Of Cylinder

Question 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

Question 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

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Note:

Students can solve the Surface Area of Cuboid by using these formulas mentioned in above section of the page. Aspirants can make this page as bookmark by pressing CTRL+D keys from keyboard.

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