##### Chapter 5

## Mensuration

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

#### Introduction

Mensuration is considered a branch of mathematics that talks about the length, volume, or area of various geometric forms. In 2 or 3 dimensions, these forms exist. Let’s learn the contrast between the two.

2D Shape | 3D Shape |

If three or more straight lines in a plane surround a shape, then it is a 2D shape. | If a shape is surrounded by a variety of surfaces or planes, then a 3D shape is concerned. |

Such forms have no height or width. | These are often referred to as solid forms that have height or width, unlike 2D. |

Such types have only two dimensions, such as length and width. | As they have a width (or height), width, and length, they are considered three dimensional. |

We may quantify their perimeter and area. | They can be measured by length, CSA, LSA, or TSA. |

Let’s learn a few more definitions relating to this topic.

Terms | Abbreviation | Unit | Definition |

Area | A | m^2 or cm^2 | The area is the surface which is covered by the closed shape. |

Perimeter | P | m or cm | The measure of the continuous line along the boundary of the given figure is called a Perimeter. |

Volume | V | cm^3 or m^3 | The space occupied by a 3D shape is called a Volume. |

Curved surface area | CSA | m^2 or cm^2 | If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere |

Lateral surface area | LSA | m^2 or cm^2 | The total area of all the lateral surfaces that surrounds the given figure is called the Lateral Surface area. |

Total surface area | TSA | m^2 or cm^2 | The sum of all the curved and lateral surface areas is called the Total Surface area. |

Square unit | – | m^2 or cm^2 | The sum of all the curved and lateral surface areas is called the Total Surface area. |

Cube unit | – | cm^3 or m^3 | The volume occupied by a cube of one side one unit |

Let’s now learn all the significant calculation formulas that involve 2D and 3D shapes. Using this list of measurement formulas, it is easy to solve the problems of measurement. Students can also download the PDF list of measuring formulas from the link given above. In general, surface area and volumes of 2D and 3D figures are the most common formulas for calculation.

2D measuring deals with the measurement of different dimensions such as area and circumference of 2-dimensional forms such as square, rectangular, circle, triangle, etc.

The analysis and estimation of surface area, lateral surface area, and volume of 3-dimensional figures such as a cube, sphere, cuboid, cone, disk, etc. are concerned with 3D measurement.

**Area and Perimeter of Triangles **

There are three types of triangles namely scalene, isosceles, and right-angled triangle.

**Scalene Triangle**

- Area of scalene triangle: √[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2
- The perimeter of a scalene triangle: a+b+c

**Isosceles Triangle**

- Area of isosceles triangle: ½ × b × h
- The perimeter of an isosceles triangle: 2a + b

**Right Angled Triangle**

- Area of a right-angled triangle: ½ × b × h
- The perimeter of a right-angled triangle: b + hypotenuse + h

**Area and Circumference of a Circle **

- Area of a circle: πr^2
- Circumference of a circle: 2πr

**Area and Perimeter of Quadrilaterals**

The following quadrilaterals have been listed for their area and perimeter.

**Square**

- Area of a square: a^2
**The perimeter of a square: 4a**

**Rectangle**

- Area of rectangle: l x b
**Perimeter of rectangle:2(l + b)**

**Rhombus**

- Area of rhombus: ½ × d1 × d2
**The perimeter of rhombus: 4 x side**

**Parallelogram**

- Area of parallelogram: (b x h)
**Perimeter of parallelogram: 2 x (l + b)**

**Trapezium**

- Area of trapezium: ½ h (a + c)
- Perimeter of trapezium: (a + b + c + d)

In this chapter, we learned about the basics of **mensuration**. We learned about the different 2D shape formulas for their area and perimeter. We also learn the **areas of combination of figures**. We will use this knowledge and solve the figures for their areas and perimeters.

**1. What is mensuration? **

Mensuration is the ability to quantify the length of lines, surface areas, and volumes of solids from the basic line and angle data. It is commonly used when geometric figures are concerned, where different physical quantities such as perimeter, area, volume, or length have to be calculated.

**2. What is the mensuration formula? **

A measurement function is essentially a formula based on other specified dimensions, regions, etc. to calculate the length-related properties of an entity (such as area, circumradius, etc., of a polygon).

**3. What are the types of mensuration? **

- Cylinder.
- Circles.
- Polygons.
- Rectangles and Squares.
- Trapezium, Parallelogram and Rhombus.
- Area and Perimeter.
- Cube and Cuboid.

**4. What is the importance of mensuration? **

Mensuration, when it comes to the geometry of the universe, is a very interesting topic. Mensuration applies, by extension, to the portion of geometry associated with deciding distances, regions, and volumes. It is also easy to understand that calculating is instrumental and plays a significant role in real-world applications.

**5. What is the history of mensuration?**

The Ancient Egyptians developed and developed an efficient land survey, leveling, and calculation techniques and used mathematics to deal with these measurement methods. Mensuration is a branch of mathematical science that is concerned with the calculation of different geometric figures for areas and quantities.

Explore more about **mensuration **through simple, interactive, and explanatory visualizations, download the MSVgo – the Math Science Super App which focuses on conceptual clarity.