NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.2 Part 5

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Image gives herons formula in simple terms

Herons Forumla in Simple Terms

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Art derived from Herons Formula

Herons Formula Illustration

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Q-8 A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being (see Fig). Find the cost of polishing the tiles at the rate of

A Floral Design Made of Triangles


  • Semi perimeter of each of the triangular shapes

  • Therefore, area of each of the triangular tiles

  • Therefore, total area of

  • Cost of polishing tiles =

  • Therefore, total cost of polishing tiles

Q-9 A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. find the area of the field.


SBQP is the Required Trapezium


  • SBQP be the trapezium with parallel sides and the non-parallel sides


  • Draw

  • Draw , therefore QPSR is now a parallelogram


  • and

  • .

  • Therefore, semi perimeter of the

Therefore, by Herons formula, area of the

Area of the parallelogram

Therefore, area of the trapezium