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lateral triangle withA traffic signal board, indicating 'SCHOOL AHEAD' is an equside 'a Find the area of the signal board, using Heron's formula. If its perimeter is180 cm, what will be the area of the signal board?1. |
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Answer» Length of the side of equilateral triangle = aPerimeter of the signal board = 3a = 180 cm∴ 3a = 180 cm ⇒ a = 60 cmSemi perimeter of the signal board (s) = 3a/2Using 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 = √3/4 × 60 × 60 = 900√3cm2 |
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