How do you find the length of an equilateral triangle with the perimeter?

h = altitude

*Length units are for your reference only since the value of the resulting lengths will always be the same no matter what the units are.

Calculator Use

An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. The altitude shown h is hb or, the altitude of b. For equilateral triangles h = ha = hb = hc.

If you have any 1 known you can find the other 4 unknowns. So if you know the length of a side = a, or the perimeter = P, or the semiperimeter = s, or the area = K, or the altitude = h, you can calculate the other values. Below are the 5 different choices of calculations you can make with this equilateral triangle calculator. Let us know if you have any other suggestions!

Formulas and Calculations for a equilateral triangle:

• Perimeter of Equilateral Triangle: P = 3a
• Semiperimeter of Equilateral Triangle: s = 3a / 2
• Area of Equilateral Triangle: K = (1/4) * √3 * a2
• Altitude of Equilateral Triangle h = (1/2) * √3 * a
• Angles of Equilateral Triangle: A = B = C = 60°
• Sides of Equilateral Triangle: a = b = c

1. Given the side find the perimeter, semiperimeter, area and altitude

• a is known; find P, s, K and h
• P = 3a
• s = 3a / 2
• K = (1/4) * √3 * a2
• h = (1/2) * √3 * a

2. Given the perimeter find the side, semiperimeter, area and altitude

• P is known; find a, s, K and h
• a = P/3
• s = 3a / 2
• K = (1/4) * √3 * a2
• h = (1/2) * √3 * a

3. Given the semiperimeter find the side, perimeter, area and altitude

• s is known; find a, P, K and h
• a = 2s / 3
• P = 3a
• K = (1/4) * √3 * a2
• h = (1/2) * √3 * a

4. Given the area find the side, perimeter, semiperimeter and altitude

• K is known; find a, P, s and h
• a = √ [ (4 / √3) * K ] = 2 * √ [ K / √3 ]
• P = 3a
• s = 3a / 2
• h = (1/2) * √3 * a

5. Given the altitude find the side, perimeter, semiperimeter and area

• h is known; find a, P, s and K
• a = (2 / √3) * h
• P = 3a
• s = 3a / 2
• K = (1/4) * √3 * a2

For more information on triangles see:

Weisstein, Eric W. "Equilateral Triangle." From MathWorld--A Wolfram Web Resource. Equilateral Triangle.

Weisstein, Eric W. "Altitude." From MathWorld--A Wolfram Web Resource. Altitude.

ΔABC is an equilateral triangle with area 55. 

Find the perimeter (to the nearest tenth).

Possible Answers:

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.

ΔABC is an equilateral triangle with area 28. 

Find the perimeter (to the nearest tenth).

Possible Answers:

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.

An equilateral triangle has a side length of

What is the perimeter of the triangle?

Possible Answers:

Correct answer:

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

An equilateral triangle has a side length of

What is the perimeter of the triangle?

Possible Answers:

Correct answer:

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

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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.

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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.

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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.

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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.

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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.

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

Find the perimeter of the figure.

Possible Answers:

Correct answer:

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 

Recall that the side lengths in a 

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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