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

Answer:

Since, the sign board is an equilateral triangle so it's each side will be equal.

Let the side of the equilateral triangle be 'a' cm.

Given, Perimeter of equilateral triangle = 180 cm

Perimeter = side + side + side [ For 3 sides of triangle ]

a + a + a = 180

3a = 180

a = 180/3 = 60 cm

Now, s = $\tt{\dfrac{a + b + c}{2}}$

Here, b and c are equal to 'a' due to being an equilateral triangle ( all sides equal ).

s = $\tt{\dfrac{a + a + a }{2}}$

s = $\tt{\dfrac{60 + 60 + 60}{2}}$

s = 90

Using Heron's Formula,

Area of the signal board, A = $\sqrt{\tt{s ( s - a) ( s - b) ( s - c )}}$

A = $\sqrt{\tt{s ( s - a) ( s - a) ( s - a )}}$

A = $\sqrt{\tt{90 ( 90 - 60) ( 90 - 60) ( 90 - 60 )}}$

A = $\sqrt{\tt{90 ( 30) (30) ( 30 )}}$

A = $\sqrt{\tt{30* 30( 30) (30) ( 30 )}}$

A = 900 $\tt{\sqrt{3 } cm^2}$

Answer 2

Answer:

900 √(3)

Step-by-step explanation: