NCERT Class 9 Solutions: Heron՚S Formula (Chapter 12) Exercise 12.1 Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Herons Formula with Semi-Perimeter

Q-1 A traffic signal board, indicating ‘SCHOOL AHEAD’ , is an equilateral triangle with side ‘a’ . Find the area of the signal board, using Heron՚s formula. If its perimeter is 180 cm, what will be the area of the signal board?


  • Length of equilateral triangle
  • Perimeter of the signal board
  • Semi perimeter of the signal board (s)
  • Using heron՚s formula
  • Area of the signal board

Q-2 The triangular side walls of a flyover have been used for advertisements. The sides of the walls are (see Fig) . The advertisements yield on earning of per year. A company hired one of its walls for 3 months. How much rent did it pay?

Triangular Side Walls Used for Advertisement, Side of Wall a …


Given, the sides of the triangle are

  • Perimeter of the triangle is ()
  • Semi perimeter of triangle (s) ()
  • Using heron՚s formula,
  • Area of the advertisement

Rate of advertising rent per year =

Therefore, Rent of one wall for 3 months =

Q-3 There is a slide in a park. One of its side walls has been painted in some color with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig) . If the sides of the wall are finding the area painted in colour.

Slide in a Park


  • Sides of the triangular wall are
  • Semi perimeter of triangular wall (s)
  • Using heron՚s formula, area of the message

Q-4 Find the area of a triangle two sides of which are and the perimeter is


  • Two sides of the triangle
  • Perimeter of the triangle
  • Third side of triangle ()
  • Semi perimeter of triangle
  • Using heron՚s formula,
  • Area of the triangle