The formula for a regular triangle area is equal to the squared side times the square root of 3 divided by 4: Show
and the equation for the height of an equilateral triangle looks as follows:
But do you know where the formulas come from? You can find them in at least two ways: deriving from the Pythagorean theorem (discussed in our Pythagorean theorem calculator) or using trigonometry. 1. Using Pythagorean theorem
One leg of that right triangle is equal to height, another leg is half of the side, and the hypotenuse is the equilateral triangle side.
2. Using trigonometry
Instructor: Yuanxin (Amy) Yang Alcocer Show bio Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted. An equilateral triangle is a triangle that has three sides of the same length. Explore the steps in finding the area of an equilateral triangle and learn to calculate the area through solved examples. Updated: 01/05/2022 Steps to SolveTo find the area of an equilateral triangle, or a triangle with 3 equal sides, all you have to do is to follow these steps. Step 1Use this formula for the area of an equilateral triangle: Area FormulaIn this case, the upper case A is the area and the lower case a is the length of the sides, which again, are all equal, hence the same letter being used. Step 2Plug in your value for the length of a side of your equilateral triangle and evaluate. That is it! With a simple formula like this, calculating the area is really easy. Just plug in to the formula and evaluate! Let's see this in action.
Finding the AreaFind the area of this equilateral triangle. ProblemStep 1The first step is to remember the formula, which is the square root of 3 divided by 4 multiplied by the square of the side of the equilateral triangle. Area FormulaStep 2The next step is to plug in the value for the side of the equilateral triangle. For this triangle, the side is 3 inches long. So, you plug in 3 for the variable s. Square that and you get 9. Multiplying the 9 by the square root of 3 and dividing by 4, you get 3.9 inches squared. And you are done! Another ExampleLet's try another one. Find the area of an equilateral triangle with sides that measure 6 centimeters. Step 1First, write down the formula. The square root of 3 divided by 4 multiplied by the square of the side of the equilateral triangle. Step 2Your side measures 6 centimeters, so you plug in 6 to the formula. 6 squared is 36. Multiplying that by the square root of 3 and dividing by 4, you get 15.6 centimeters squared. And you are done. Register to view this lessonAre you a student or a teacher? Unlock Your EducationSee for yourself why 30 million people use Study.comBecome a Study.com member and start learning now.Become a Member Already a member? Log In Back Resources created by teachers for teachersOver 30,000 video lessons & teaching resources‐all in one place. Video lessons Quizzes & Worksheets Classroom Integration Lesson Plans I would definitely recommend Study.com to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline. Back Create an account to start this course today Used by over 30 million students worldwide Create an account How do you find the area of a triangle with 3 equal sides?If a triangle has 3 equal sides, it is called an equilateral triangle. The area of an equilateral triangle can be calculated using the formula, Area = a2(√3/4), where 'a' is the side of the triangle.
How do you find the area of a equilateral triangle with height?Equilateral triangle area and height. Using Pythagorean theorem. The basic formula for triangle area is side a (base) times the height h , divided by 2: area = (a × h) / 2. ... . Using trigonometry. Let's start with the trigonometric triangle area formula: area = (1/2) × a × b × sin(γ) , where γ is the angle between the sides.. |