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#### Definition Of Cube And Cuboid: Lateral Surface Area Of Cube

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### Definition of cube and cuboid

Definition of Cuboid- Cuboid is a shape that has three dimension and it is a three dimensioned geometrical figure that is generally bounded by the six rectangular regions. The below diagrams shows the diagram of a cuboid.

Definition of Cube- the definition of a cube can be defined as a solid that have equal length, breadth, as well as height that are all to be equal in measurement. It is a solid bounded six square planes that has regions on all the sides and all the side of the cube are known as the edges.

### Cuboid Properties

Faces included in cuboid- A cuboid is generally made of six rectangles in the cube and each of the rectangle on the cube is called the face. In the figure shown above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are 6 faces that can be shown in cuboid.

The top surface of the cuboid and the bottom face of the pair are the opposite faces. Similarly, there are pairs that have opposite faces and the adjacent faces that are opposite to one another is known as the adjacent faces of the cuboid.

The base as well as the lateral faces that are included in the cuboid include any face that includes base of the cuboid. There are four faces in the cuboid that are adjacent to base and that are known as the lateral face of cuboid. The surface that are on the solid actually rests on the base of a solid.

The edges are known as the cuboid which is in line segment that comes between two adjacent vertices. In a cuboid there are 12 edges. The edges in a cuboid are AB, AD, AE, HD, HE, HG, GF, GC, FE, FB, EF and CD and they are opposite sides for the rectangle that are equal with the cuboid. The vertices included in a cuboid mainly includes three point of intersection that include three edges that are included in a cuboid. These are commonly known as the vertex of the particular cuboid.

### Formula of cube and cuboid

Surface area formulas of a cuboid-

The total surface area of a cuboid is calculated as the total sum of the areas that are included in six rectangular faces. For deriving the formulas, let us consider a length to be l and the breadth of the cuboid is as b. the height of the cuboid is considered to be as h.

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

### Surface area of a cube

For calculating the total surface area of the cube, let us consider the side of the cube as the l. So the formula that are included in the cube states cube

Surface of cube = 2 (l * l + l * l + l * l) = 6 * l * l

### Lateral surface area for the cuboid

The sum for the surface area included in all the sides includes top as well as bottom of the face of solid that is generally defined as the lateral surface area of that solid.

Lateral surface area of that cuboid = total area of all the faces that is Area of the face ADHE + Area of the face BCGF + Area of the face ABFE + Area of the face DCGH = 2 ( b × h ) + 2 ( l × h ) = 2 h ( l + b ).

Lateral surface are of the cuboid is 2 * h ( l + b )

Lateral surface area of cube

2 ( l × l + l × l ) = 4 * l2

Diagonal of the cuboid =√ ( l2 + b2 + h2 )

Perimeter of a cuboid = 4 ( l + b + h )

Diagonal of a cube = √3 * l

Perimeter of a cube = 12 * l

### Lateral surface area for the cube

Cube has four sides and the area of the cube is considered to be as of equal. A cube has four sides that can be considered as s in the cube. The cube has all equal sides. As it is discussed above that the cube is the solid that have breadth, length as well as height of the cube. The cube has six regions and there are ides in each side. The lateral surface area of the cuboid is considered with six sides that includes length, breadth as well as height of the cube. The formula of lateral surface area of the cube is considered to be 2 ( l * l + l * l ) = 4 * l * l = 4l2

The formula of the surface area of the cube is 6 * l * l.

An example of finding out the surface area of cube and the lateral surface area of cube is stated below:

Let us consider that the cube having its side to be 8 cm.

Length of the cube = 8 cm

The surface area of the cube = 6 * l * l = 6 * 8 * 8 = 6 * 64 = 438 cm2

The lateral surface area of the cube = 4 * l * l = 4 * 8 * 8 = 4 * 64 = 256 cm2

Another example of finding out the surface area of cube and the lateral surface area of cube is stated below:

Let us consider that the cube having its side to be 4 cm.

Length of the cube = 4 cm

The surface area of the cube = 6 * l * l = 6 * 4 *4 = 6 * 16 = 96 cm2

The lateral surface area of the cube = 4 * l * l = 4 * 4 * 4 = 4 * 16 = 64 cm2

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