Question

4.
Find the area of an equilateral triangle whose one side is 6
cm long​

Answer 1

Refer the attachment above ..

Hope it Helps !!

Answer 2

Given:-

• Side of an equilateral triangle = 6 cm

To find:-

• Area of the triangle

Solution:-

There are two methods of solving this question.

1st method is by heron's formula:-

To find the area of a triangle using Heron's formula, we first need to find the semi-perimeter of the triangle.

We know,

$\sf{Semi - Perimeter = \dfrac{a+b+c}{2}}$

Since, all the sides of an equilateral triangle are equal,

$\sf{s = \dfrac{6 + 6 + 6}{2}}$

= $\sf{s = \dfrac{18}{2}}$

= $\sf{s = 9}$

Now,

Applying Heron's Formula,

$\sf{Area = \sqrt{s(s-a)(s-b)(s-c)}\:sq.units}$

= $\sf{Area = \sqrt{9(9-6)(9-6)(9-6)}{cm}^{2}}$

= $\sf{\:\:\:\:\:\:\: = \sqrt{9\times3\times3\times3}{cm}^{2}}$

= $\sf{\:\:\:\:\:\:\: = \sqrt{3\times3\times3\times3\times}{cm}^{2}}$

= $\sf{\:\:\:\:\:\:\:\: = 3\times3\sqrt{3}{cm}^{2}}$

= $\sf{\:\:\:\:\:\:\:\: = 9\sqrt{3} {cm}^{2}}$

2md method :-

We know,

$\sf{Area\: of\: an \: equilateral \: triangle = \dfrac{\sqrt{3}{a}^{2}}{4}sq.units}$ [Where a = side of the triangle]

Therefore,

$\sf{Area = \dfrac{\sqrt{3}{(6)}^{2}}{4}{cm}^{2}}$

= $\sf{\:\:\:\: = \dfrac{\sqrt{3}\times{36}}{4}{cm}^{2}}$

= $\sf{\:\:\:\: = 9\sqrt{3}{cm}^{2}}$