Question

. 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

SOLUTION                                                                                                           Length of the side of equilateral triangle = a
Perimeter of the signal board = 3a = 180 cm
∴ 3a = 180 cm ⇒ a = 60 cm
Semi perimeter of the signal board (s) = 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
                                       = √3/4 × 60 × 60 = 900√3 cm2

Answer 2

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Length of the side of equilateral triangle = a

Perimeter of the signal board = 3a = 180 cm

∴ 3a = 180 cm ⇒ a = 60 cm

Semi perimeter of the signal board (s) = 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

= √3/4 × 60 × 60 = 900√3 cm2.