Draw 3 radii, and then 3 new lines that bisect the radii. You get six 30-60-90 triangles.

These triangles can be used ot find a side length .

Using the formula for the area of an equilateral triangle in terms of its side, we get

Draw out 3 radii and 3 lines to the corners of each triangle, creating 6 30-60-90 triangles.

See that these 30-60-90 triangles can be used to find side length.

Formula for side of equilateral triangle is

.

Now substitute the new equation that is in terms of R in for S.

To solve, simply multiply the side length by 3 since they are all equal. Thus,

To solve, simply multiply the side length by . Thus,

To solve, simply multiply the side length by . Thus,

To solve, simply multiply the side length by 3 since they are all equal. Thus,

Draw out 3 radii and 3 lines to the corners of each triangle, creating 6 30-60-90 triangles.

See that these 30-60-90 triangles can be used to find side length.

Formula for side of equilateral triangle is

.

Now substitute the new equation that is in terms of R in for S.

Draw 3 radii, and then 3 new lines that bisect the radii. You get six 30-60-90 triangles.

These triangles can be used ot find a side length .

Using the formula for the area of an equilateral triangle in terms of its side, we get

While you can very quickly compute the area of an equilateral triangle by using a shortcut formula, it is best to understand how to analyze a triangle like this for other problems. Let's consider this. The shortcut will be given below.

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of to is the same as the ratio of to .

As an equation, this is written:

Solving for , we get:

Now, the area of the triangle is merely . For our data, this is: or .

Notice that this is the same as . This is a shortcut formula for the area of equilateral triangles.

While you can very quickly compute the area of an equilateral triangle by using a shortcut formula, it is best to understand how to analyze a triangle like this for other problems. Let's consider this. The shortcut will be given below.

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of to is the same as the ratio of to .

As an equation, this is written:

Solving for , we get:

Now, the area of the triangle is merely . For our data, this is: or .

Notice that this is the same as . This is a shortcut formula for the area of equilateral triangles.