The Concept of Mensuration

What is mensuration? 

Mensuration as a concept can be directly linked to the measurement of objects, both 2D and 3D. This subfield of geometry deals with various functions of 2D and 3D objects such as area, volume, length, and width. The field of mensuration has no set rules as people could use nonstandard units of measurements such as measuring their yard by walking around it and counting the steps. 

There are standard units of measurement present which make the topic easier. It’s important to remember that while using nonstandard units of measurement there is always a big chance for human error. It’s always better to use standard units such as meters, kilometers, liters, etc.  

One dimensional figure

Such shapes which have only one measurement are known as one-dimensional figures. A straight line connecting a point to another point can be seen as a one-dimensional figure.  

Two-dimensional figures

Such shapes or figures which have two measurements are known as two-dimensional figures. They are also known as 2D figures. The two measurements that two-dimensional figures have are usually length and breadth. Examples of two-dimensional figures are square, rectangle, triangle, rhombus, etc.  

Three-dimensional figures

Such figures or shapes have three measurements and are known as three-dimensional figures. In addition to the length and breadth of the two-dimensional figures, the three-dimensional figures also have another measurement in the form of height or depth. Some examples of three-dimensional objects are balls, tanks, bats, and books. Some of the three-dimensional figures used in geometry are sphere, cube, cone, etc.  

Important terminologies in mensuration

Area: area could be defined as all the space present in a closed section of space. Such spaces could be enclosed by definitive boundaries. The symbol for the area is A. square unit is the measurement unit for the area.  

Volume

In a three-dimensional closed shape or object, the space present in such shapes is known as the volume of the object. The unit for volume is cubic-meter and is denoted by the alphabet V.  

Perimeter

Perimeter can be defined as the complete length of the boundary of a shape or a figure. Perimeter is present only in two-dimensional shapes and figures. The unit used to measure perimeter is square-unit and is represented by the alphabet P.  

Surface area

The total area which is being occupied by a three-dimensional object is known as the surface area of the object. There are two further types of surface area which are lateral surface area and total surface area.  

Important mensuration formulas

Here are some of the important mensuration formulas that will come in handy: 

Rectangle

Being a 2D shape, a rectangle has 4 sides and the same number of corners. All angles at the corner of the rectangle are right angles.  

Perimeter: 2 [ L + B ] where L is length and B is the breadth  

Area: [ L X B ] where L is length and B is the breadth  

Square

Square is a 2D shape, it has equal sides and they are 4 in number. Each angle in a square is 90 degrees. 

Area: [ S X S ] where S is a side 

Perimeter: 4 [ S ] where S is a side  

Circle

Circle is another 2D shape, and each point on the circle is equidistant from the center of the circle.  

Diameter of the circle: 2 X R, where R is the radius of the circle  

Circumference of the circle: 2 X π X R, where R is the radius of the circle and π is a constant.  

Area of the circle: π X R X R. where R is the radius of the circle and π is a constant.  

Sphere

It is a 3D object, which means it has depth or height. The sphere is a geometric shape and all points on the sphere are equidistant to its center.  

The volume of a sphere: 4/3 X π X R X R X R, where R is radius and π is a constant.  

The surface area of a sphere: 4 X π X R X R, where R is radius and π is a constant.  

Conclusion

Mensuration is a concept in geometry that deals with various figures and shapes. We looked at the types of figures in single, double, and triple dimensions. Furthermore, we looked at some important terminologies and mensuration formulas. These were some of the most fundamental concepts of Mensuration. Be sure to conduct a thorough research online to avail more information about this concept.