  Quick Math Homework Help
Master the 7 pillars of school success 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?

​h = √3/2 * a   a =side
6=√3/2 * a
a = 6/√3/2
a =4√3

Common Core Standard  6.G.1     Triangle Practice Problems

### The formula for Height of an Equilateral Triangle  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.
Side Length  This formula works for all polygons
s= length of one side
n = number of sides
tan = tan function in degrees Side Length  Side Length
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.
• The height is equal to side/2 x √3