Question

find the area of a triangle whose all sides are equal and sum of the 3 sides is equal to 12cm....
.......... please give answer now I'm in class

Answer 1

$\huge{Hey\:Mate\:Here\:Is\:Your\:Answer}$

$\textbf{Given That .....}$

There Is A Triangle Whose All Sides Are Equal And Some Of The Sides Is Equal To 12cm . We Need To Find

The Area of The Triangle..

So Let's Move To Solution ...

$\textbf{Solution ....}$

According To The Question It's Given That The All Sides Of The Triangle Are Equal and Their Sum Is Equal To

12 centimetre.

Now To Find It's Area Of Triangle Follow The Simple Steps ....

$\underline\bold{1)) First\: To \:Find\: Length \:Of \:All \:Sides.....}$

So Let The Length Of Side of Triangle = X

$\textbf{So The Sum Of Sides = X + X + X = 12}$

That Is ...

$3x = 12cm$

Now Taking 3 To RHS We Have ....

$x = \frac{12}{3}$

Therefore We Have ....

$x = 4cm$

Hence The Length Of The Sides Are ...

$4cm$

$\underline\bold{2)) \:So\: Now \:To \:Find\: The\: Area \:Of\: Triangle\: Whose\: all\: sides\: are \:3cm ..}$

We Have A Formula Called The $\textbf{Heron's Formula }$ That Is ....

$\boxed{\boxed{ \sqrt{s(s - a)(s - b)(s - c)} } }$

⏺️ Where " S " Is The Half Of The Perimeter ... And a , b & c Are the sides of Triangle

So Here Perimeter = 12cm. ( Given )

Therefore Half of Perimeter = 12/2 = 6cm

Hence

$\textbf{S = 6cm}$

So Now The sides a,b & c We Have

$\textbf{a = b = c = 4cm}$

⏺️As It's Given That All Sides Are Equal

Now Putting Values Of a, b & c And " S " In Formula We Have ....

$\boxed{\sqrt{ \: 6(6 - 4)(6 - 4)(6 - 4)} }$

That Is ---

$\sqrt{6(2)(2)(2)}$

Now We Can split 6 As 2 × 3 So We Have...

$\sqrt{(2) \times (3)(2)(2)(2)}$

$\sqrt{(3) ({2}^{2}) \times ({2}^{2} ) }$

That Is Equal To ....

$4 \sqrt{3} \: {cm}^{2}$

$\textbf{Hence The Area Of Triangle Is}$

$\boxed{\boxed{= \:4\sqrt{3}\: Or \:6.93 \:cm^2 ( Approx )} }$

$\large{# Be \: Brainly }$

Answer 2

Given: Sides of the triangle are equal and its perimeter adds up to 12cm.

To find: The area.

Answer:

Heron's Formula: √s(s - a)(s - b)(s - c)

Since all the sides are equal, let a, b and c be x.

x + x + x = 12cm

3x = 12cm

x = 12/3

x = 4cm

a + b + c/2 = Semi - Perimeter (s)

4 + 4 + 4/2 = 12/2 = 6cm

s - a = 6 - 4 = 2cm

s - b = 6 - 4 = 2cm

s - c = 6 - 4 = 2cm

Area of the triangle = √s(s - a)(s - b)(s - c)

= √6*2*2*2

= √2*3*2*2*2

= 2*2√3

= 4√3cm^2

Hope it helps :)