## Measurement formulas

These formulas are applied to measure ratios of a specific quantity. It is derived by comparing one quantity with the conventional unit. The fundamental measurements are area, mass, volume, and distance.

Measurement formulas are there to assist us in finding the basic measurements using the provided parameters. This category of formulas also comprises a few conversion formulas such as the conversion of meter to miles, an inch into feet, etc.

## What are the measurement formulas?

For various objects, we get separate measurement formulas. These formulas are indispensable when you wish to calculate the parameters of certain objects. The dimension of any object is either 2 dimensional or 3 dimensional. Below we have listed the measurement formulas for different shapes.

### Table of measurement formulas applicable to 2-dimensional shapes

Shape Type | Measurement of area | Measurement of perimeter |

Rectangle | Length x breadth square units | 2 x (length + breadth) |

Square | (Measurement of a side)2 | 4 x measurement of any side |

Triangle | ½ x base x altitude square units | Sum of three sides |

Parallelogram | Height x base square units | 2(a+b) |

Isosceles Trapezoid | ½ x h(a+b) square units | a + b + c + d |

Circle | Πr2 square units | 2 Πr |

Rhombus | ½ x 1st diagonal x 2nd diagonal square units | 4 x measurement of any side |

For 3-D shapes, we can evaluate the total surface area, length and volume.

### Table of measurement formulas applicable to 3-dimensional shapes

Shape Type | Total surface area | Length or lateral surface area | Volume |

Cube | 6a2 | 4a2 | a3 |

Cuboid | 2 x (length x breadth + breadth x height + height x length) | 2. height (breadth + length) | Length x height x breadth |

Cone | Πr(r+l), here r is the radius of the cone’s base. | Πrl Here, l is the slant height of the cone. | 1/3 Πr2h |

Sphere | 4 Πr2 | – | 4/3 Πr3 |

Cylinder | 2 Πr(h+r ) | 2Πrh | Πr2h |

Prism | Lateral surface area x (2x base area) | Height x base perimeter | Base x height |

Pyramid | Base area + lateral surface area | ½ perimeter x slant height | 1/3 x h x B |

### Solved Examples

Junaid measured that each side of a square is 6cms. Calculate its area using measurement formulas.

**Solution:** According to the measurement formulas, area of square = a2

Here the value of a is 6cms.

Therefore, area of the square is (6cm)2 or, 36cm2.

**Answer:** 36cm2

Apply the measurement formulas to determine the area of the circle that has a radius of 11 units.

**Solution:** Area of any circle = r2Π sq. units

= 112 x Π sq. units

= 379.94 sq. units

**Answer:** 379.94 sq. units.