Question

EXERCISE 12.1
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?​

Answer 1

Answer:

heya ✌✌

The perimeter of a triangle is equal to the sum

of its three sides it is denoted by 2S.

2s=(a+b+c)

s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

 

The formula given by Heron about the area of a

triangle is known as Heron's formula. According to this formula area of a

triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle

and s is a semi perimeter.

 

This formula can be used for any triangle to

calculate its area and it is very useful when it is not possible to find the height

of the triangle easily . Heron's formula is 

generally used for calculating area of scalene triangle.

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 Solution:

Given, side of a

signal whose shape is an equilateral triangle= a

Semi perimeter, s=a+a+a/2=

3a/2

Using heron’s

formula,

Area of the signal board = √s (s-a) (s-b) (s-c)

= √(3a/2) (3a/2 – a) (3a/2 – a) (3a/2 –

a)

= √3a/2 × a/2 × a/2 × a/2

= √3a⁴/16

= √3a²/4

Hence, area of signal board with

side a by using Herons formula is= √3a²/4

 

Now,

Perimeter of an equilateral

triangle= 3a

Perimeter of the traffic signal board = 180 cm  (given)

 3a = 180 cm

 a = 180/3= 60 cm

Now , area of

signal board=√3a²/4

= √3/4 × 60 × 60

= 900√3 cm²

Hence , the area

of the signal board when perimeter is 180 cm is 900√3 cm².

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Hope this will help you....