Question

if perimeter is 240cm,then find the area of the signal board

a)1600 cm^2 b)1600√3 cm^2 c)800 cm^2 d)800 √3 cm^2​

Answer 1

Answer:

Ans. For an equilateral triangle with side ‘a’, area

∴ Each side of the triangle = a cm

∴ a + a + a = 180 cm

⇒ 3a = 180 cm

Now, s = Semi–perimeter

∴ Area of a triangle

∴ Area of the given triangle

Thus, the area of the given triangle

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Answer 2

Given:

Perimeter is 240cm

Solution:

Know that a signal board has a shape of a equilateral triangle.

Therefore,

$\[\begin{array}{l}3a = 240\;{\rm{cm}}\\ \Rightarrow a = 80\,{\rm{cm}}\end{array}\]$

Know that area of equilateral triangle is given by,

$\[ = \frac{{\sqrt 3 }}{4}{a^2}\]$

$\[\begin{array}{l} = \frac{{\sqrt 3 }}{4} \times {80^2}\\ = \sqrt 3 \times 20 \times 80\\ = 1600\sqrt 3 \,{\rm{c}}{{\rm{m}}^2}\end{array}\]$

Hence, the area of the signal board is $\[1600\sqrt 3 \,{\rm{c}}{{\rm{m}}^2}\]$.