NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.1 Part 1
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Q1 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

Perimeter of the signal board

Semi perimeter of the signal board (s)

Using heron's formula
Area of the signal board

Q2 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?
Solution:
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 =
Q3 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.
Solution:

Sides of the triangular wall are

Semi perimeter of triangular wall (s)

Using heron's formula, area of the message

Q4 Find the area of a triangle two sides of which are and the perimeter is
Solution:

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
