Inside the Article

**Mensuration Formulas For 2D And 3D Shapes :** Solving mensuration problems and searching for the formulas to solve these questions easily, so you are at the right place. Here, we have provided you all the mensuration formulas for 2D and 3D shapes in the table below. You can go through them and take the help of these mensuration formulas for 2D and 3D shapes to solve the problems easily.

We hope that you are aware of the term ‘Mensuration’ and if not, then it is at all not an issue. We will help you out to understand the meaning of this term. So, mensuration is a branch of mathematics which deals with the measurement of different shapes and figures of geometry. Measurement means that you can use the formula of the particular shape and find out its area or volume or perimeter, or anything that you want to calculate.

Maths Formulas for Class 10 all Type of Important Formulas pdf

In the table below, we have first provided you with the mensuration formulas to calculate 2D shapes and next is the table that provides you with the formulas to calculate 3D shapes. Down below we have also provided you with the details that what all figures fall under the category of 2D shapes and what are figures are there that fall under the category of 3D.

### Mensuration Formulas For 2D Shapes

Shape |
Area (Square units) |
Perimeter (units) |
---|---|---|

Square |
a² | 4a |

Rectangle |
l × b | 2 ( l + b) |

Circle |
πr² | 2 π r |

Scalene Triangle |
√[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2 | a+b+c |

Right Angle Triangle |
½ × b × h | b + hypotenuse + h |

Parallelogram |
b × h | 2(l+b) |

Isosceles Triangle |
½ × b × h | 2a + b |

Equilateral Triangle |
(√3/4) × a² | 3a |

Rhombus |
½ × d1 × d2 | 4 × side |

Trapezium |
½ h(a+b) | a+b+c+d |

### Mensuration Formulas For 2D And 3D Shapes

This article provides you with a list of mensuration **formulas** for 2D and 3D shapes. Go through the article and learn a lot of mensuration formulas like area of parallelogram, perimeter of isosceles triangle and many more. But before proceeding, let us first learn about what all are the figures that fall under the category of 2D figures and 3D figures.

**2D Shapes : **So, these are the flat plane shapes that has only two dimensions – length and breadth. These figures do not have any thickness and can only be measured in two faces. You can only calculate area and perimeter of 2D shapes. These include – square, rectangle, circle, parallelogram, equilateral triangle and many more discussed below.

**3D Shapes :** These are the three dimensional figures and have length, width, and thickness. These are made using X-axis, Y-axis, and Z-axis. You can calculate curved surface area, total surface area, and volume of these 3D figures. These figures include – cube, cuboid, cone, sphere, hemisphere, cylinder, and many more.

### Mensuration Formulas For 3D Shapes

Shape |
Volume (Cubic units) |
Curved Surface Area (CSA) orLateral Surface Area (LSA) (Square units) |
Total Surface Area (TSA) (Square units) |
---|---|---|---|

Cube |
a³ | 4 a² | 6 a² |

Cuboid |
l × b × h | 2 h (l + b) | 2 (lb +bh +hl) |

Cone |
(⅓) π r² h | π r l | πr (r + l) |

Sphere |
(4/3) π r³ | 4 π r² | 4 π r² |

Cylinder |
π r² h | 2π r h | 2πrh + 2πr² |

Hemisphere |
(⅔) π r³ | 2 π r² | 3 π r² |

** Example Questions :**

**Q. Find the area of a trapezium whose parallel sides are 15 cm and 19 cm long, and the distance between them is 20 cm.**

**Solution**: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)

= 1/2 (15 + 19) * (20)

= 340 cm^{2}

**Q. Find the area of a parallelogram with a base of 14 cm and a height of 26 cm.**

**Solution**: Area of a parallelogram = base * height

= 14 * 26

= 364 cm^{2}

**Q. PQRS is a rectangle. The ratio of the sides PQ and QR is 3 : 1. If the length of the diagonal PR is 10 cm, then what is the area (in cm²) of the rectangle?**

**Solution :** PQRS is a rectangle

PR = 10 (given)

PQ : QR = 3 : 1

In ∆PQR

9x² + x² = 100

10x² = 100

x = √10

Area of rectangle = 3x × 1x

= 3x²

= 3 × 10

= 30 cm²

**Q. Find the volume of a cone, if the radius is 4 cm and height is 9 cm.**

**Solution : **Radius r = 4 cm

Height h = 9 cm

Using the volume of a cone formula,

Volume of cone = (⅓) π r² h

Volume of cone* = *1/3 x 3.14 x 4 x 4 x 9

= 150.72 cm³

**Q. What is the volume of the largest sphere that can be carved out of a cube of edge 3 cm?**

**Solution :** The diameter of the sphere is equal to the length of the edge of the cube

∴ the radius of the sphere r = 3/2

Volume of the sphere is given by = (4/3) π r³

= 4/3 x π x 3/2 x 3/2 x 3/2 = 9π/2

=4.5π cm^{3}

We hope that the list of Mensuration formulas for 2D and 3D figures that we have provided above in the article will help you a lot in solving mensuration problems. In case of queries you may use the comment box and drop your queries there.