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.
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An equilateral triangle is a triangle with all sides equal and all angles equal to 60°.
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.
Our area of an equilateral triangle calculator find the area of an equilateral triangle showing you all the working out along the way.
Example 1) Find the area of the equilateral triangle below. Give your answer to 1dp.
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.
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.
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.
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.
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:
\[ A = {1 \over 2} s ({ \sqrt 3 \over 2} s) \]
\[ A = { \sqrt 3 \over 4} s^2 \]
Take a look at some more of our worksheets similar to these.
Our printable support page has the formulas for the area of common 2d shapes.
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:
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:
All the math practice worksheets in this section support Elementary Math Benchmarks.
Here is our range of volume worksheets.
Using these sheets will help your child to:
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