- Enter the values of Side of the triangle or Area of the Triangle

- Click on the calculate button to get the value of empty

if a is side of the triangle,then Area,Height and Perimeter is given

$A = \frac {a^2 \sqrt 3}{4}$

$p =3a$

$h = \frac { a \sqrt 3}{2}$

Equilateral triangle is a triangle where all the side are equal. The perpendicular from the vertices to the Opposite sides divides the side.

Area of the Equilateral triangle can be calculated using Heron formula which is

$A = \sqrt { s(s-a)(s-b)(s-c)}$ where $s = \frac {a +b +c}{2}$

Now for equilateral triangle

a=b=c=a

Therefore

$s = \frac {a +b +c}{2}= \frac {3a}{2}$

$A=\sqrt { s(s-a)(s-b)(s-c)} = \sqrt {\frac {3a}{2} ( \frac {3a}{2} -a) ( \frac {3a}{2} -a)( \frac {3a}{2} -a)} = \frac {a^2 \sqrt 3}{4}$

Perimeter of the Equilateral triangle is given by

$p = 3a$

Now Height can be calculated

We know that Area is also given as

$A = \frac {1}{2} ah$

Therefore

$\frac {1}{2} ah= \frac {a^2 \sqrt 3}{4}$

$h = \frac { a \sqrt 3}{2}$

Find the Area ,Height and Perimeter of a Equilateral Triangle whose side is.

i. 4 cm

ii. 12 cm

(i) a = 4 cm

Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4} = \frac {4^2 \sqrt 3}{4}= 4 \sqrt {3} \ cm$

Height is calculated as

$h = \frac { a \sqrt 3}{2}= \frac { 4 \sqrt 3}{2}=2 \sqrt {3} \ cm$

Perimeter of the Equilateral triangle is given by

$p = 3a = 3 \times 4 = 12 \ cm$

(ii) a = 12 cm

Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4} = \frac {(12)^2 \sqrt 3}{4}= 36 \sqrt {3} \ cm$

Height is calculated as

$h = \frac { a \sqrt 3}{2}= \frac { 12 \sqrt 3}{2}=6 \sqrt {3} \ cm$

Perimeter of the Equilateral triangle is given by

$p = 3a = 3 \times 12 = 36 \ cm$

Find the Side,Perimeter and Height of a Equilateral Triangle whose Area is.

i. $400 \sqrt 3$ cm

ii. $100 \sqrt 3$ cm

(i) A = $300 \sqrt 3$ cm

Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4} = \frac {4^2 \sqrt 3}{4}= 4 \sqrt {3} \ cm$

Rearranging for Side

$a = \sqrt {\frac {4A}{\sqrt 3}}= \sqrt { \frac {4 \times 400 \sqrt 3}{\sqrt 3}}= 40 \ cm$

Height is calculated as

$h = \frac { a \sqrt 3}{2}= \frac { 40 \sqrt 3}{2}=20 \sqrt {3} \ cm$

Perimeter of the Equilateral triangle is given by

$p = 3a = 3 \times 40 = 120 \ cm$

(ii) A = $100 \sqrt 3$ cm

Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4} = \frac {4^2 \sqrt 3}{4}= 4 \sqrt {3} \ cm$

Rearranging for Side

$a = \sqrt {\frac {4A}{\sqrt 3}}= \sqrt { \frac {4 \times 100 \sqrt 3}{\sqrt 3}}= 20 \ cm$

Height is calculated as

$h = \frac { a \sqrt 3}{2}= \frac { 20 \sqrt 3}{2}=10 \sqrt {3} \ cm$

Perimeter of the Equilateral triangle is given by

$p = 3a = 3 \times 20 = 60 \ cm$

- Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4}$

- Height is calculated as

$h = \frac { a \sqrt 3}{2}$

- Perimeter of the Equilateral triangle is given by

$p = 3a$

- Side of Equilateral Triangle is calculated as

$a= \sqrt {\frac {4A}{\sqrt 3}} $

- Height is calculated as

$h = \frac { a \sqrt 3}{2}$

- Perimeter of the Equilateral triangle is given by

$p = 3a$

- Side of Equilateral Triangle is calculated as

$a= \frac {p}{3} $

- Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4}$

- Height is calculated as

$h = \frac { a \sqrt 3}{2}$

- Side of Equilateral Triangle is calculated as

$a= \frac {2h}{\sqrt 3} $

- Area of Equilateral Triangle is calculated as

$A= \frac {a^2 \sqrt 3}{4}$

- Perimeter of the Equilateral triangle is given by

$p = 3a$

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