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?

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Answer 1

Answer:

Given Perimeter =180 cm

Semi-perimeter s=

2

180

s=90 cm

Since all sides of equilateral triangle are equal

So,

Perimeter =180

a+a+a=180

3a=180

a=60 cm

Area of triangle =

s(s−a)(s−b)(s−c)

=

90(90−60)(90−60)(90−60)

=

90×30×30×30

=

(9×3×3×3)×(10)

4

=

(9

2

)×3×(10)

4

=9×

3

×(10)

2

=9×100×

3

=900

3

Answer 2

$\huge \bold \color{red} \mathfrak \star{\underbrace \green {answer}} \star$

$\bold {\underline\blue{given \: perimeter}} \: = 180cm$

$\bold {\underline \blue{semi \: perimeter(s)}} = \frac{180}{2} \\ s \: = 90cm$

we know that..all the sides of equilateral triangle are equal..

let the all sides of triangle are a

perimeter = 180cm

$\bold { = > a + a + a = 180} \\ \\ \bold { = > 3a \: = 180 \: \: \: \: \: \: \: \: \: \: \:} \\ \\ \bold { = > a = \frac{180}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold { \: = > a = 60} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now...area of triangle by heron's formula..

$area= \sqrt{s(s - a)(s - b)(s - c)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: : \: \: \: \: \: \: \\ \\ area = \sqrt{90(90 - 60)(90 - 60)(90 - 60)} \: \: \: \: \: \: \: \: \\ \\ area = \sqrt{90 \times 30 \times 30 \times 30} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: : \: \: \: \: \\ \\ area \: = \sqrt{3 \times 30 \times 30 \times 30 \times 30} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: \\ \\ area = 30 \times 30 \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ area = 900 \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bold {\color{purple} \underline \orange{ar(triangle)}} = 900 \sqrt{3} {cm}^{2}$

so..area of signal board is 900√3cm²

✌️☺️