1. A traffic signal board, indicating SCHOOLAHEAD', is an equilateral

1.	1. A traffic signal board, indicating SCHOOLAHEAD', is an equilateral triangle withside 'a Find the area of the signal board, using Heron's formula. If its perimeter is180 em, what will be the area of the signal board?12.3 A
Answer» Solution: Given, side of asignal whose shape is an equilateral triangle= a Semi perimeter, s=a+a+a/2=3a/2 Using heron’sformula, 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 withside a by using Herons formula is= √3a²/4 Now, Perimeter of an equilateraltriangle= 3a Perimeter of the traffic signal board = 180 cm (given) 3a = 180 cm a = 180/3= 60 cm Now , area ofsignal board=√3a²/4 = √3/4 × 60 × 60 = 900√3 cm² Hence , the areaof the signal board when perimeter is 180 cm is 900√3 cm². ================ hit like if you find it useful

1. A traffic signal board, indicating SCHOOLAHEAD', is an equilateral triangle withside 'a Find the area of the signal board, using Heron's formula. If its perimeter is180 em, what will be the area of the signal board?12.3 A

Answer»

Solution:

Given, side of asignal whose shape is an equilateral triangle= a

Semi perimeter, s=a+a+a/2=3a/2

Using heron’sformula,

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

Now,

Perimeter of an equilateraltriangle= 3a

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

3a = 180 cm

a = 180/3= 60 cm

Now , area ofsignal board=√3a²/4

= √3/4 × 60 × 60

= 900√3 cm²

Hence , the areaof the signal board when perimeter is 180 cm is 900√3 cm².

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