Cuboid-Surface Area

“Cuboid” is a significant geometrical figure in mathematics and the study is based on analysing the formula of the surface area of a cuboid. The document will consist of a clear description on the concept of a cuboid and the formula that helps in finding out the surface area of a cuboid. A number of examples will be added to make the understanding better and frequently asked questions will be added at the end as well to provide answers to some relatable queries. 

Cuboid surface area

What is a cuboid?

In mathematics, a “cuboid” refers to a figure that is three dimensional and it is bounded with six rectangular planes. It has different magnitudes in case of length, height and width. Anything around that has a rectangular shape can be identified as a cuboid and it is possible for a cuboid to be developed by a number of rectangles of various dimensions in case it is observed from a specific ending line. A cuboid is a three dimensional figure whereas a rectangular is a two dimensional figure, however they share a significant connection. A “cuboid” consists of six rectangular sides and these are called faces. Each corner of the face signifies the measurement of 90 degrees. The cuboid includes 12 edges in total and overall 8 vertices. The opposite sides or faces of a cuboid are always equal to the other side. 

The further points will focus on the cuboid surface area and at the time of discussing this, it is important to emphasise total surface area as well as lateral surface area. These surface areas are measured as per square units and the volume of the cube is measured as per the cubic units. 

Concept of cuboid surface area and the related formulas

It is important to discuss the area of a cuboid before discussing the surface area of a cuboid. The area of a cuboid signifies the surface area and it is because a cuboid is a three dimensional solid figure. From this concept, it can be asserted that the area of a cuboid can be measured with the help of the formula of the area of a rectangle. It has been previously mentioned that both rectangle and cuboid share a significant connection and the reason behind using the formula of area of a rectangle in this context is that a cuboid has rectangular faces. 

The surface area of a cuboid can be divided into two types such as, total surface area and lateral surface area which is also known as curved surface area. 

Total surface area

The total surface area of a cuboid is calculated by summing up the measures of all 6 rectangular faces.

“Total surface area (TSA) = 2*(l*w+w*h+l*h) square units”

The formula for finding out the total surface area of a cuboid is 2 (lw+wh+lh) square units and here l refers to length, w refers to width and h signifies the height. The total surface area can also be considered as TSA and the formula is applicable for a cuboid that contains all the six faces. 

Lateral or curved surface area

The lateral surface area is found out by adding measures of 4 planes of a rectangular shape and in this context the upper (top) and lower (base) surfaces are not calculated in the formula. The lateral or curved surface area can be considered as LSA or CSA. The formula used in this context is 2 (lh+wh) = 2 h (l+w) square units.

“Lateral or curved surface area (LSA or CSA) = 2 (l*h+w*h) = 2*h (l+w) square units”

Total surface area of a cuboid derivation

Cuboid has 6 rectangular faces and l, w, h signify length, width and height respectively. 

Front face area= l*h

Back face area= l*h

Top face area= l*w

Bottom face area= l*w

Left face area= h*w

Right face of area= h*w

Therefore, TSA= 2lh + 2lw + 2hw = 2 (lh+lw+hw) square units.

Example of the given formula

A cuboid that has a length of 7 cm, width of 5 cm and height of 5 cm will have a total surface area (TSA) of 190 centimetre square. 

As l = 7 cm, width = 5 cm and height = 5 cm,

TSA = 2 (lw+wh=lh)

= 2 (7*5 + 5*5 + 7*5)

= 2 (35+25+35)

= 2*95

= 190 cm2

Conclusion

The entire document is based on the cuboid and the surface area of the cuboid. It has been found out during the study that two types of surface area must be focused on in this context such as Total surface area or TSA and Lateral surface area or LSA. Significant explanation of formulae and supportive examples are provided to simplify the understanding of the delivered data. There are a number of FAQs that help in determining the differences among a cube and a cuboid; and the differences among TSA and LSA. All the information will help one to understand the concept of surface area of a cuboid in a better way.