Question

a traffic signal board, SCHOOL AHEAD. is an equilateral triangle with side a find the area of the signal board using herons formula. if its perimeter is 180cm what will be the area of the signal board?​

Answer 1

Answer:

Step-by-step explanation:

Let 'a' be the side of the equilateral triangle. In equilateral triangle, all three sides are equal.

Heron's Formula = √s(s-a)(s-b)(s-c)

where s = a+b+c/2 = 3a/2 (Please note s is semi-perimeter)

Perimeter of equilateral triangle = 2s = 180 => s = 90

=> 90 = 3a/2

=> 180 = 3a

=> a = 60 cm.

Area of Equilateral triangle = √s(s-a)(s-b)(s-c)

                                              = √s(s-a)(s-a)(s-a)

                                              = √s(s-a)³                        

                                              =  √90(90-60)³

                                              = √90*(30)³

                                              = √30 * 3 * (30)³

                                              = √3 * (30)⁴

                                               = (30)² * √3 = 900√3 cm².