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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
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
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
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.