Math, asked by arjunmanoj03, 1 year ago

If the side of an equilateral triangle is 'a' centimetre then find its area using heron's formula


shreyabembalkar: a+a+a/2 =3a/2 a =3/2

Answers

Answered by Mankuthemonkey01
34
Heron's Formula is the formula used for getting the area of triangles. Heron's Formula :-
 \sqrt{s(s - a)(s - b)(s - c)}

Where, s = semi perimeter and a,b and c are sides.


So we have an equilateral triangle with all sides = a cm

So semi perimeter = (a + b + c) ÷ 2

=>
s =  \frac{a + a + a}{2}  \\  \\  =  > s =  \frac{3a}{2}

So put the value of s, a, b and c in the formula to get the area


=> area =
 \sqrt{ \frac{3a}{2}( \frac{3a}{2}   - a)( \frac{3a}{2}  -a )( \frac{3a}{2} - a) }

=
 \sqrt{ \frac{3a}{2}( \frac{a}{2}  )( \frac{a}{2} )( \frac{a}{2}) }


=
 \sqrt{ \frac{ {3a}^{4} }{16} }  \\  \\  =   \frac{ \sqrt{3}  \:  \:  {a}^{2} }{4}

Hence the area of equilateral triangle =
 \frac{ \sqrt{3} }{4}  {a}^{2}  \\

khan973: Hii
Answered by ShadowplayerLC
10

Answer:


Step-by-step explanation:

s= (a+a+a)/2

s= 3a/2

ar=root [s(s-a)(s-b)(s-c)]

ar= root [3a/2 *( 3a/2 - a) * (3a/2 - a) * (3a/2 - a)]

ar = root [3a/2 * a/2 * a/2 * a/2]

ar = root[ 3 * a/2 * a/2 * a/2 * a/2]

ar = a^2/4 root[3]

ar = \frac{\sqrt 3}{4} * a^2

         

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