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

s = (a+a+a)/2

s=3a/2

where a is the length of the side.

Now, as per the heron’s formula, we know;

Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Since, a = b = c

Therefore,

A = √[s(s-a)3]

which is the required formula.

Answer 2

Answer:

Given => equilateral triangle (side a,a,a)

Perimeter = 180 cm

.

=> perimeter = a+a+a

.

=> 180 = 3a

.

=> a = 60cm

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now area of the equilateral triangle =

.

=> s =

$\frac{a + b + c}{2}$

=> s =

$\frac{60 + 60 + 60}{2}$

=>s =

$\frac{180}{2}$

=> s = 90

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Area =

$\sqrt{s(s - a)s(s - b)s(s - c)}$

Area=

$\sqrt{90(90 - 60)90(90 - 60)90(90 - 60)}$

Area=

$\sqrt{90(30)(30)(30)}$

Area=

$30 \sqrt{90 \times 30}$

Area=

$30 \sqrt{3 \times 30 \times 30}$

Area=

$30 \times 30 \sqrt{3}$

Area=

$90 \sqrt{3}$

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