# Intermediate Geometry : How to find the area of an equilateral triangle

## Example Questions

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### Example Question #701 : Plane Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #701 : Plane Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #261 : Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #701 : Intermediate Geometry

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #42 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #43 : How To Find The Area Of An Equilateral Triangle

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #69 : Equilateral Triangles

An equilateral triangle is placed on top of a regular hexagon as shown by the figure below.

Find the area of the entire figure.

Explanation:

Recall that a regular hexagon can be divided into  congruent equilateral triangles.

Since the extra equilateral triangle on top has the same side lengths as of the equilateral triangles made by dividing the hexagon, the entire figure has a total of  congruent equilateral triangles.

Thus, to find the area of the entire figure, we must first find the area of the equilateral triangle.

Recall how to find the area of an equilateral triangle:

Plug in the length of a side of the equilateral triangle.

Now, multiply this area by  to find the area of the entire figure.

Make sure to round to  places after the decimal.

### Example Question #70 : Equilateral Triangles

The cube in the above diagram has edges of length 1. Give the area of .