Question

The perimeter of an equilateral triangle is 60 cm, then its area is​

Answer 1

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 :

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

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

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

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

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

Answer 2

Question :

To find area of a equilateral Triangle.

Solution :

Given ::

• Perimeter of triangle = 60 cm

Perimeter of a equileteral triangle is by adding all sides of triangle.

Let , side be a

$➝\sf \: a + a + a \: = 60 \\ \\ ➝ \: \sf \: 3a \: = 60 \\ \\ ➝\sf \: a = \frac{60}{3} \\ \\ ➝\sf \: a \: = 20$

Length of sides of triangle is 20 cm.

To find area of equilateral Triangle ::

${\underline{\boxed{\bf{area \: of \: Triangle \: = \sqrt{s(s - a)(s - b)(s - c)} }}}}$

• a , b , c = sides of triangle

• s = semiperimetre

• Semi perimeter is the half of perimeter

$\sf \bullet \: \: semi \: Perimeter \: = \frac{60}{ 2} \\ \\ \sf➝ \: 30$

Area :

$\sf \: ➝ \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf \: ➝ \: \sqrt{30(30 - 20)(30 - 20)(30 - 20)} \\ \\ ➝ \: \sqrt{30 \times 10 \times 10 \times 10} \\ \\ </p><p>➝\sf \sqrt{3 \times 10 \times 10 \times 10 \times 10} \\ \\ \sf \: ➝10 \times 10 \sqrt{3} \\ \\ \bf \: ➝100 \sqrt{3}$

Area of Triangle = 100√3 cm²