Question

if the perimeter of an equilateral triangle is 60 cm then what is its area.​

Answer 1

$\huge\bold\red{ solution }$

given ;

perimeter of an equilateral triangle = 60 cm

to find ;

area of an equilateral triangle ????

proof ;

perimeter of an equilateral triangle = 3a

$60 = 3a \\ (where \: a \: is \: side) \\ \\ a = \frac{60}{3} \\ = 20cm \:$

side of an equilateral triangle = 20 cm

$area = \frac{ \sqrt{3} }{4} a ^{2} \\ \\ area = \frac{ \sqrt{3} }{4} \times 20 \times 20 \\ \\ area = 100 \sqrt{3}$

Answer 2

Step-by-step explanation:

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 :

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

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

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

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

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