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Let's look at several more examples of finding the height of an equilateral triangle.

Find the height of an equilateral triangle with side lengths of 8 cm.

8/2 = 4 4√3 = 6.928 cm.

When do you use decimals and when do you use the answer with a square root. The answer with the square root is an exact answer. On standardized tests like the SAT they expect the exact answer. The decimal answer is an estimate.

Find the height of an equilateral triangle with sides of 12 units.

12/2 = 6 then 6√3 units = 10.392 units

An equilateral triangle has a side of 16 units. What is the height of this equilateral triangle.

16/2=8√3 units or 13.856 units

The height of an equilateral triangle is 10 units. What is the side length?

Find the height of a triangle with sides of 6 units.

Step 1. Take 1/2 of a side times √3

6/2* √(3 )=3√3 = height

The formula for Area of an Equilateral Triangle

1/2 base * height or 1/2 b * h

Find the area of a equilateral triangle with a side of 8 units

Step 1. Use the height formula: (side/2 * √3 ) to calculate the height.

height = 8/2* √3=4√3

Step 2. Plug height into the area formula 1/2b * h

h=1/2 (8)(4√3 )=16√3 = area of triangle

The formula for Perimeter of an Equilateral Triangle

Perimeter = Add all three sides or 3* side

What is the perimeter of a triangle with a side of 7 units ?

Add all three sides 7+7+7 = 21 units

or

3(7) = 21 units

Apothem length formula is as follows:

Find the apothem of an equilateral triangle with sides of 12 units

Step 1. Plug the side length in the formula

12/((2√3 ) )

Step 2. Simplify 12/(2√3 ) =

units = Apothem

Side Length

Side Length

Finding the height of an equilateral triangle

The apothem is the distance from the center of the polygon to the midpoint of a side

Video solution to finding the height

Video solution to finding the apothem

Apothem

In this case we have a triangle so the Apothem is the distance from the center of the triangle to the midpoint of the side of the triangle. The Apothem is perpendicular to the side of the triangle, and creates a right angle.

There are many different types of triangles named by their side length, and angle measure. An equilateral triangle has the following properties.

Equilateral triangles have three equal side lengths

Equilateral triangles also have three equal angles of 60 degrees

They also have three equal altitudes

Is the height of an equilateral triangle equal to its side length. No It is easy to imagine with everything being equal that the height, and the side length would be equal, but they are not.