NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.1 Part 1

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Herons formula with semi-perimeter

Herens Formula in Two Parts

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?

Solution:

  • Length of equilateral triangle Equation

  • Perimeter of the signal board Equation

  • Semi perimeter of the signal board (s) Equation Equation

  • Using heron's formula

    Area of the signal board

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

Q-2 The triangular side walls of a flyover have been used for advertisements. The sides of the walls are Equation (see Fig). The advertisements yield on earning of Equation 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 are 122m,22m and 120m

Triangular Side Walls Used for Advertisement

Triangular side walls used for advertisement, side of wall are 122m,22m and 120m

Solution:

Given, the sides of the triangle are Equation

  • Perimeter of the triangle is Equation ( Equation )

  • Semi perimeter of triangle (s) Equation ( Equation )

  • Using heron's formula,

    Area of the advertisement

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

Rate of advertising rent per year = Equation

Therefore, Rent of one wall for 3 months = Equation

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 Equation finding the area painted in colour.

Triangle poly1 Triangle poly1: Polygon A, B, C Segment c Segment c: Segment [A, B] of Triangle poly1 Segment a Segment a: Segment [B, C] of Triangle poly1 Segment b Segment b: Segment [C, A] of Triangle poly1 Segment f Segment f: Segment [C, D] Segment g Segment g: Segment [A, E] Segment h Segment h: Segment [D, E] Segment i Segment i: Segment [B, F] Segment j Segment j: Segment [E, F] Vector u Vector u: Vector[G, H] Vector u Vector u: Vector[G, H] Vector v Vector v: Vector[I, J] Vector v Vector v: Vector[I, J] Vector w Vector w: Vector[K, L] Vector w Vector w: Vector[K, L] Vector d Vector d: Vector[M, N] Vector d Vector d: Vector[M, N] 11m text1 = "11m" 15m text2 = "15m" 6m text3 = "6m" KEEP THE PARK GARDEN AND CLEAN text4 = "KEEP THE PARK GARDEN AND CLEAN" KEEP THE PARK GARDEN AND CLEAN text4 = "KEEP THE PARK GARDEN AND CLEAN"

Slide in a Park

Slide in a park, its side painted in some message “KEEP THE PARK GREEN AND CLEAN”.

Solution:

  • Sides of the triangular wall are Equation

  • Semi perimeter of triangular wall (s) Equation

  • Using heron's formula, area of the message

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

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

Solution:

  • Two sides of the triangle Equation

  • Perimeter of the triangle Equation

  • Third side of triangle Equation ( Equation )

  • Semi perimeter of triangle Equation Equation

  • Using heron's formula,

    Area of the triangle

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

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