Question

Plzz tell if u know.............plzz answer in long with full explanation.....​

Answer 1

Step-by-step explanation:

Given -

• A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’.
• Perimeter = 180 cm

To Find -

• Area of the signal board, using Heron's formula.

As we know that :-

• All sides of equilateral triangle are equal
• Perimeter of equilateral triangle = 3a

where, a = side of triangle

→ a + a + a = 180

→ 3a = 180

→ a = 60

And

As we know that :-

• s = a + b + c/2

→ a + a + a/2

→ 3a/2

Then,

Area of triangle = √s(s-a)(s-b)(s-c)

→ √3a/2(3a/2-a)(3a/2-a)(3a/2-a)

→ √3a/2(3a-2a/2)(3a-2a/2)(3a-2a/2)

→ √3(a/2)(a/2)(a/2)(a/2)

→ √3a²/4

Now,

Substituting a = 60

Area =

→ √3×60×60/4

→ 60×15×√3

→ 900√3 cm²

Hence,

The area of signal board is 900√3 cm².

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ 900√3cm²

$\large\underline\mathrm{Given:-}$

the equilateral triangle with side 'a'.

perimeter = 180cm

$\large\underline\mathrm{To \: find}$

area of the signal board using hero's formula.

all sides of equilateral triangle are equal.

perimeter of equilateral triangle = 3a

$\large\underline\mathrm{Solution}$

$\implies$ a + a + a = 180°

$\implies$ 3a = 180°

$\implies$ a = 60°

$\large\underline\mathrm{and}$

$\implies$ s = a + b + c/2

$\implies$ a + a + a/2

$\implies$ 3a/2

$\large\underline\mathrm{Area \: of \: triangle}$

$\implies$ √s(s - a)(s - b)(s - c)

$\implies$ √3a/2(3a/2 - a)(3a/2 - a)(3a/2 - a)

$\implies$ √3a/2(3a/2 - 2a/2)(3a/2 - 2a/2)(3a/2 - 2a/2)

$\implies$ √3(a/2)(a/2)(a/2)

$\implies$ √3a²/4

$\large\underline\mathrm{Now,}$

$\large\underline\mathrm{put \: the \: \: value \: of \: a \: = \: 60}$

$\large\underline\mathrm{Area}$ $\implies$ √3a²/4

$\implies$ √3 × 60 × 60/4

$\implies$ √3 × 15 × 60

$\implies$ 900√3cm²

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$