Question

the perimeter of an equilateral triangle is 60cm. what is its area?

Answer 1

Perimeter = 60cm 
1 side = 60/3 = 20 cm
√s(s-a)(s-b)(s-c)s(s−a)(s−b)(s−c) 

s = 30 

√30(30-20)(30-20)(30-20)

=√30×10×10×10=√30000cm² = 100√3 cm²

Answer 2

Answer:

$100\sqrt{3}cm^{2}$ is the required area of an equilateral triangle .

Step-by-step explanation:

Explanation:

Given , perimeter of an equilateral triangle = 60cm

Equilateral triangle : A triangle with all three sides  equal  and also there  three angles are   equal. Each angle is 60 °

Let 'a' be the side of an equilateral triangle

Step 1:

Therefore , Perimeter of an equilateral triangle = 3a

⇒ 3a = 60  (perimeter of a equilateral triangle is 60cm given )

⇒$a = \frac{60}{3} = 20 cm$

Area of a equilateral triangle = $(\frac{\sqrt{3} }{4} )a^{2}$

⇒ Area = $(\frac{\sqrt{3} }{4} )(20)^{2}$ = $(\frac{\sqrt{3} }{4} )400$

⇒ Area = $100\sqrt{3}$$cm^{2}$ .

Final answer :

Hence , area of an equilateral triangle of side 20cm is $100\sqrt{3}cm^{2}$

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