Area of an Equilateral Triangle Calculator: Grasping the step by step process of calculating the Area of an Equilateral Triangle helps students to solve the Math problems easily in their higher classes. Equilateral Triangle Area Calculator is a free online tool that calculates the solution for given inputs within a fraction of seconds. This calculator aids to save students valuable time while solving tough and difficult math problems. So, find the Area of an Equilateral Triangle in a short span with our easy to use Area of an Equilateral Triangle Calculator tool.
By this online calculator, you can make your math calculations easier and faster with accurate results. Also, you can understand the calculation of the Area of an equilateral triangle by going through with our detailed explanation and solved examples. However, you may also learn what is Area of an equilateral triangle and how you can calculate the area from here.
What is meant by Area of an Equilateral Triangle?
The area of an equilateral triangle is defined as the amount of space that remains on a 2D closed surface. Firstly, remember that an equilateral triangle is a triangle where all of its sides are equal and the measurement of all the internal angle is 60º. All the angles in an equilateral triangle are congruent. As triangle is a 2D figure it has both area and perimeter.
Thus, finding an equilateral triangle area is very easy if you have the length of its side. Apply the side value in the formula of area of an equilateral triangle and get the area for the Math problems.
Formula of Area of an Equilateral Triangle
The formula for the area of an equilateral triangle is given as:
| Area of Equilateral Triangle (A) = (√3/4)s2 or (√3/4)a2 |
Where s and a represent length of sides.
Derivation of Area of an Equilateral Triangle
First, take an equilateral triangle of the side as ‘a’ unit. Then all sides of a triangle are ‘3a’ now draw a perpendicular bisector to the base of height ‘h’.
Now take the Area of Triangle formula i.e., Area = ½ × base × height
Here, we are assuming base = a, and height = h
Now, apply Pythagoras Theorem in the triangle.
a2 = h2 + (a/2)2
⇒ h2=a2–a2/4
⇒ h2=(3a2)/4 Or h=½(√3a)
Now, put the value of ‘h’ in the area of the triangle equation.
So, Area of Triangle = ½ × base × height
⇒ A = ½ × a × ½(√3a)
Thus, Area of Equilateral Triangle = ¼(√3a2) or (√3/4)a2
How to Calculate the Area of an Equilateral Triangle?
If you know the side of an equilateral triangle, then apply the input in the formula of area of an equilateral triangle
ie., Area of an Equilateral Triangle (A) = (√3/4)a2
Where ‘a’ is the length of any side of the triangle.
OR
Note that √3/4 is constant that has a value of approximately 0.433, so the formula of an Area of an Equilateral Triangle is A = 0.433a2. (approximately).
Solved Example
Question 1: What is the area of an equilateral triangle whose side is 3.7 cm?
Solution:
Given that side = 3.7 cm
Area of an Equilateral Triangle (A) = (√3)/4 × a2
Put the value of side in Area Formula.
Area= (√3)/4 × 3.72
⇒ Area = (√3)/4 x 3.7 x 3.7
Multiply 3.7 cm and 3.7 cm
⇒ Area = (√3)/4 x 13.69
⇒ Area = 1.732/4 x 13.69
⇒ Area = 0.433 x 13.69
⇒ Area= 5.92777 cm2
Therefore, Area of an Equilateral Triangle side 3.7 cm is 5.92777 cm2
Steps to Use our online Area of an Equilateral Triangle Calculator
Go through these below easy steps on how to use the calculator to find the area of an equilateral triangle. By using our handy Equilateral Triangle Area Calculator, you can make your calculations extremely easier and faster. So, follow these simple steps and find the area of an equilateral triangle for any type of unit you required.
- Enter the Equilateral Triangle Side in the input field.
- After that, choose the required Unit metric for a triangle side as cm,m, ft, yd, mi, etc. from the dropdown list.
- Later click on the ‘Area’ button which is located below to the input box.
- Finally, you will get the output on the screen along with a detailed explanation.
FAQs on Equilateral Triangle Area Calculator
1. What is the Formula for Area of Equilateral Triangle?
The formula to find the area of an equilateral triangle is A = ¼(√3a2).
2. What is the Formula for Perimeter of the Equilateral Triangle?
The formula to calculate the perimeter of an equilateral triangle is P = 3a
3. What is the area of an equilateral triangle whose side is 5 cm?
Area of an Equilateral Triangle (A) = (√3)/4 × a2
⇒ (√3)/4 × 52
⇒ (√3)/4 × 5 × 5
⇒ (√3)/4 × 25.0
⇒ 0.433 x 25.0
Area= 10.825 cm2
4. How to find the area of an equilateral triangle whose all sides are equal?
If you are given any of the sides of a triangle which are equally measured, then you can find the area of the equilateral triangle using basic formula i.e. Area = (√3)/4 × a2