Question

find the area of an equilateral triangle using heron's formula the length of each side is 'a' units

Answer 1

EXPLANATION.

Area of an equilateral triangle using heron's formula.

Length of each side = a units.

As we know that,

Formula of

semi-perimeter = a + b + c/2.

Semi-perimeter = a + a + a/2. = 3a/2.

Formula of :

Heron's formula = √s(s - a)(s - b)(s - c).

⇒ √3a/2(3a/2 - a)(3a/2 - a)(3a/2 - a).

⇒ √3a/2(3a - 2a/2)(3a - 2a/2)(3a - 2a/2).

⇒ √3a/2(a/2)(a/2)(a/2).

⇒ √3a⁴/16 = √3a²/4 sq. units.

Answer 2

Step-by-step explanation:

To find:-

Area of a equilateral triangle using herons Formula.

Herons Formula:-

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

Solution:-

Let side be a

Semi perimeter:-

$\\ \tt{:}\dashrightarrow \dfrac{a+a+a}{2}$

$\\ \tt{:}\dashrightarrow \dfrac{3a}{2}$

Area:-

$\\ \tt{:}\dashrightarrow \sqrt{s(s-a)(s-b)(s-c)}$

$\\ \tt{:}\dashrightarrow \sqrt{\dfrac{3a}{2}(\dfrac{3a}{2}-a)(\dfrac{3a}{2}-a)(\dfrac{3a}{2}-a)}$

$\\ \tt{:}\dashrightarrow \sqrt{\dfrac{3a}{2}(\dfrac{3a-2a}{2})(\dfrac{3a-2a}{2})(\dfrac{3a-2a}{2})}$

$\\ \tt{:}\dashrightarrow \sqrt{\dfrac{3a}{2}(\dfrac{a}{2})(\dfrac{a}{2})(\dfrac{a}{2})}$

$\\ \tt{:}\dashrightarrow \sqrt{\dfrac{3a}{2}\times \dfrac{a^3}{8}}$

$\\ \tt{:}\dashrightarrow \sqrt{\dfrac{3a^4}{16}}$

$\\ \tt{:}\dashrightarrow \dfrac{3a^2}{4}$