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

## Example Questions

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### Example Question #1 : How To Find The Perimeter Of An Equilateral Triangle

ΔABC is an equilateral triangle with area 55.

Find the perimeter (to the nearest tenth).

35.9

40.3

39.1

37.2

33.8

33.8

Explanation:

To find the perimeter of an equilateral triangle given its area, we must first find the length of the sides. This can be done by using the equation of the area of an equilateral triangle:

where a is the side of the triangle.

Because the sides of the equilateral triangle are equal, the perimeter is equal to 3a.

### Example Question #2 : How To Find The Perimeter Of An Equilateral Triangle

ΔABC is an equilateral triangle with area 28.

Find the perimeter (to the nearest tenth).

26.7

20.8

24.1

19.3

25.8

24.1

Explanation:

To find the perimeter of an equilateral triangle given its area, we must first find the length of the sides. This can be done by using the equation of the area of an equilateral triangle:

where a is the side of the triangle.

Because the sides of the equilateral triangle are equal, the perimeter is equal to 3a.

### Example Question #3 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle has a side length of  cm.

What is the perimeter of the triangle?

Explanation:

The perimeter of a triangle is the sum of all three sides.

Because an equilateral triangle has all three sides of equal length, we have

### Example Question #4 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle has a side length of  cm.

What is the perimeter of the triangle?

Explanation:

The perimeter of a triangle is the sum of all three sides.

Because an equilateral triangle has all three sides of equal length, we have

### Example Question #5 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown by the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

### Example Question #1 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown by the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

### Example Question #7 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown by the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

### Example Question #8 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown by the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

### Example Question #9 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown in the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

### Example Question #10 : How To Find The Perimeter Of An Equilateral Triangle

An equilateral triangle is placed together with a semicircle as shown by the figure below.

Find the perimeter of the figure.

Explanation:

In order to find the perimeter of the entire figure, we will need to find the lengths of the segments highlighted in red.

Notice that the side length of the equilateral triangle is equal to the diameter of the semicircle.

Next, you should recall that the height of an equilateral triangle splits the triangle into two congruent  triangles.

Recall that the side lengths in a  triangle are in a  ratio. Thus, the radius of the circle, which is also the base of the  triangle, the height of the triangle, and the side length of the triangle are in the same ratio.

We can then set up the following to determine the length of the side of the equilateral triangle:

Rearrange the equation to solve for the length of the side.

Plug in the length of the height to find the length of the side.

Since the diameter of the semi-circle and the length of a side of the equilateral triangle are the same, we can write the following equation:

We have two sides of the equilateral triangle and the circumference of a semi-circle.

Plug in the length of the side to find the perimeter.

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