Area of Equilateral Triangle

Welcome to our Area of Equilateral Triangle page.

Here you will find support and worked examples to show you how to find the area of an equilateral triangle.

We also have some worksheets to help you practice this skill.

These sheets are aimed at children of a 6th grade and up.

Area of an Equilateral Triangles

What is Area?

  • Area is the amount of space that is inside a shape.
  • Because it is an amount of space, it has to be measured in squares.
  • If the shape is measured in cm, then the area would be measured in square cm or cm2
  • If the shape is measured in inches, then the area would be measured in square inches or in2

What is an Equilateral Triangle?

equilateral triangle example 1

An equilateral triangle is a triangle with all sides equal and all angles equal to 60°.

Area of an Equilateral Triangle Formula

Formula for the Area of an Equilateral Triangle

\[A = { \sqrt 3 \over 4} s^2 \]

where A is the area, and s is the length of the side of the triangle.

Area of an Equilateral Triangle Calculator

Our area of an equilateral triangle calculator find the area of an equilateral triangle showing you all the working out along the way.

Area of Equilateral Triangle Calculator

regular polygon images


Answer


Answer

 
 


How the Calculator Works

  1. Choose the number of sides of the regular polygon you need.
  2. Choose the length and width of the regular polygon: you can choose a whole number, decimal or fraction.
    • You can type a fraction by typing the numerator then '/' then the denominator.
    • You can type a mixed number by typing the whole-number part, then a space then the fraction part.
    • Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
  3. Choose your units of measurement (default is none)
  4. Choose your desired accuracy (default is 2 decimal places)
  5. Click the Find Area button
  6. You will be shown the area as a decimal (and also a fraction if you typed the length as a fraction).

Area of Equilateral Triangles Examples

Example 1) Find the area of the equilateral triangle below. Give your answer to 1dp.

area of equilateral triangle example 1

In this example the length of the side is 5 cm.

\[ So \; A = { \sqrt 3 \over 4} s^2 \]

\[ A = { \sqrt 3 \over 4} \times 5^2 \]

\[ A = 25 { \sqrt 3 \over 4} = 10.825... \; cm^2 \]

So the area of the equilateral triangle is 10.8 cm2 to 1 decimal place.

Example 2) What is the area of the yellow triangle below. Give your answer to 2dp.

area of equilateral triangle example 2

This is an equilateral triangle with side length 8 inches.

\[ So \; A = { \sqrt 3 \over 4} s^2 \]

\[ A = { \sqrt 3 \over 4} 8^2 \]

\[ A = 64 { \sqrt 3 \over 4} = 16 \sqrt 3 = 27.713... \; in^2 \]

So the area of the equilateral triangle is 27.71 in2 to 2 decimal places.

Example 3) Find the area shaded blue in the triangle below. Give your answer to 1dp.

area of equilateral triangle example 3

This is an equilateral triangle with side length 3.5 m.

\[ So \; A = { \sqrt 3 \over 4} s^2 \]

\[ A = { \sqrt 3 \over 4} (3.5)^2 \]

\[ A = 12.25 { \sqrt 3 \over 4} = 5.304... \; m^2 \]

So the area of the equilateral triangle is 5.3 m2 to 1 decimal place.

Area of Equilateral Triangles Worksheets

Area of Equilateral and Right Triangles

How To Find the Formula for the Area of Equilateral Triangles

equilateral triangle example 2

To find the area of a any triangle, you simply need to multiply the base of the triangle by the perpendicular height and halve the answer.

In this case, we will call h the perpendicular height and s the length of one side of the triangle.

You will notice that the perpendicular height bisects the base of the triangle, splitting it in half and creating two 'half' right triangles.

Let's look closer at one of these right triangles.

equilateral triangle example 3

As this is a right triangle, we can use Pythagoras' Theorem to work out the value of the height.

Pythagoras' Theorem states that the hypotenuse squared = base squared + height squared.

So substituting the values of the triangle into the equation gives us:

\[ s^2 = ({s \over 2})^2 + h^2 \]

\[ s^2 = {s^2 \over 4} + h^2 \]

\[ h^2 = s^2 - {s^2 \over 4} \]

\[ h^2 = {3 \over 4} s^2 \]

\[ h = \sqrt { {3 \over 4} s^2} \]

\[ h = { \sqrt 3 \over 2} s \]

Now we have found the height, we can use this to get the area of the triangle.

The area of a triangle is equal to half of the base multiplied by the perpendicular height.

\[ A = {1 \over 2} bh \]

where b is the length of the base, and h is the perpendicular height.

Substituting our values for the height and the base, this gives us:

\[ A = {1 \over 2} s ({ \sqrt 3 \over 2} s) \]

\[ A = { \sqrt 3 \over 4} s^2 \]

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Area of 2D Shapes Printable Support Page

Our printable support page has the formulas for the area of common 2d shapes.

More Area Worksheets

Here is our selection of free printable area worksheets for 3rd and 4th grade.

The sheets are all graded in order from easiest to hardest.

Using these sheets will help your child to:

  • work out the areas of a range of rectangles;
  • find the area of rectilinear shapes.

Perimeter Worksheets

Here is our selection of free printable perimeter worksheets for 3rd and 4th grade.

The sheets are all graded in order from easiest to hardest.

Using these sheets will help your child to:

  • work out the perimeter of a range of rectangles;
  • find the perimeter of rectilinear shapes.

All the math practice worksheets in this section support Elementary Math Benchmarks.

Volume Worksheets

Here is our range of volume worksheets.

Using these sheets will help your child to:

  • know what volume is and how to find it;
  • find the volume of shapes by counting cubes;
  • find the volume of rectangular prisms;
  • solving basic problems involving volume
 

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