Question

Hero's Formula find the area of equilateral triangle whose perimeter is 24 cm​

Answer 1

GIVEN:

★Perimeter if a equilateral∆ is 24cm.

★We have to use Herons formula.

TO FIND:

★Area of the ∆.

ANSWER:

Let us take each side be x.

Then it's perimeter

$\large{\green{Perimeter = 3a}}$

where a is the side,

=3x.

But it is given 24cm.

Atq,

=>$3x=24cm$

=>$x =\dfrac{24cm}{3}$

.°. $x = 8cm$

______________________________________

Here's the figure,

$\setlength{\unitlength}{0.78cm}\begin{picture}(12,4)\thickness\put(5.4,5.8){ A }\put(11.2,5.8){ B }\put(8.4,10){ C }\put(6,6){\line(2,3){2.5}}\put(11,6){\line(-2,3){2.5}}\put(6,6){\line(1,0){5}}\put(5,7.9){ 8\:cm }\put(11,7.9){ 8\:cm }\put(8,5){ 8\:cm }\end{picture}$

Therefore each side is 8cm long.

Now Area by Heron's Formula, =

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

where

• a, b, c are side lengths
• s is the semi perimeter
• a is the area.

So,

=>s = $\dfrac{(8+8+8) cm}{2}$

=>s =$\dfrac{24cm}{2}$

=>s= $12cm$

Let us take area be a.

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

=>$a =\sqrt{12(12-8) (12-8) (12-8) cm^{2}}$

=>$a =\sqrt{12×4×4×4cm^{4}}$

=>$a =\sqrt{2^{2}×2^{2}×2^{2}×2^{2}×3cm^{4}}$

=>$a = 2×2×2×2×\sqrt{3}cm^{2}$

. °.$a=8\sqrt{3}cm^{2}$

Therefore the area is $8\sqrt{3}cm^{2}$

Answer 2

Answer: triangle side = 3x

The perimeter = 24

3x=24

x= 24/3

x=8

Semi perimeter = a+b+c/2

8+8+8/2

24/2

12

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

√ 12× (12-8) × (12-8) × (12-8)

12× 4×4×4

2×2×3×2×2×2×2×2×2

2×2×2×2×3

16√3cm

Please mark as brilliant hope it help you