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A traffic board signal indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side $' a'$ . Find the area of the signal board using Heron’s formula. It is given that the perimeter of the triangle is $180 cm$ .

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900 c m^{2}

900 \sqrt{2} c m^{2}

900 \sqrt{3} c m^{2}

2700 c m^{2}

answer is C.

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Detailed Solution

Given,
Triangle’s perimeter

= 180 cm

Side of equilateral triangle

= a

Thus, p

erimeter,

a + a + a = 180

3 a = 180

a = 60

Area of triangle can be given as,

A = \sqrt{s (s - a) (s - b) (s - c)}

Here,

s = \frac{P}{2}

s = \frac{180}{2}

Here, each side of the triangle is equal (60 cm). Thus, by Heron’s formula,

A = \sqrt{\frac{180}{2} (\frac{180}{2} - 60) (\frac{180}{2} - 60) (\frac{180}{2} - 60)}

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

A = \sqrt{3 \times 30 \times 30 \times 30 \times 30}

A = 30 \times 30 \sqrt{3}

A = 900 \sqrt{3} c m^{2}

Hence the correct option is 3.

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