Area of Equilateral Triangle Calculator

Example of Few questions where you can use this Area of Equilateral Triangle Calculator
Question 1
Find the Area ,Height and Perimeter of a Equilateral Triangle whose side is.
i. 4 cm
ii. 12 cm
Solution
(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
$p = 3a = 3 \times 12 = 36 \ cm$

Question 2
Find the Side,Perimeter and Height of a Equilateral Triangle whose Area is.
i. $400 \sqrt 3$ cm²
ii. $100 \sqrt 3$ cm²
Solution
(i) A = $300 \sqrt 3$ cm²
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 = $100 \sqrt 3$ cm²
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
$p = 3a = 3 \times 20 = 60 \ cm$