Question

Find the area of equilateral triangle having perimeter 60 cm

Answer 1

Answer:

area of equilateral triangle is 173.21 cm²

Step-by-step explanation:

Given that, perimeter if equilateral ∆ is 60 cm

Let a be each side of equilateral ∆.

.°. a + a + a = 60 cm

=> 3a = 60

=> a = 60/3

=> a = 20 cm

Hence, eath side of equilateral ∆ is of 20 cm.

Now, we know that,

Area of equilateral ∆ = √3/4 × a²

Putting the values,

=> Area of equilateral ∆ = √3/4 × 20 × 20

=> Area of equilateral ∆ = 173.21 cm²

Hence, area of equilateral triangle is 173.21 cm²

Answer 2

Answer:

We have given that,

Perimeter = 60 cm

So, Semi Perimeter = $\dfrac{60}{2}$ = 30 cm

Hence,the Length of each side will be :]

➸ $\\ \sf a + a + a = 60$

➸ $\\ \sf 3 a = 60$

➸ $\\ \sf a = \dfrac{60}{3}$

➸ $\purple{\sf a = 20 \: cm}$

Now, we will find the area of equilateral triangle by given below formula :]

$\bigstar\:\:\boxed{\underline{\underline {\sf Area = \sqrt{s(s - a)(s - b)(s - c)}}}} \: \: \bigstar$

Now, putting the given values in above formula we get :

$: \implies\sf Area = \sqrt{30(30 - 20)(30 - 20)(30- 20)}$

$: \implies\sf Area = \sqrt{30 \times 10 \times 10 \times 10}$

$: \implies\sf Area = \sqrt{3 \times 10 \times 10 \times 10 \times 10}$

$: \implies\sf Area = 10 \times 10 \sqrt{3}$

$: \implies \underline{ \boxed{\sf Area = 100 \sqrt{3} \: cm^{2} }}$