1. Ktraflic signat hoard, indicating 'SCHOOL AHEAD', is an equilateral

1.	1. Ktraflic signat hoard, indicating 'SCHOOL AHEAD', 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?
Answer» 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

1. Ktraflic signat hoard, indicating 'SCHOOL AHEAD', 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?

Answer»

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