Polygon comes in all shapes and sizes. That is why there is no single key for finding the height of a polygon. For every shape, we require a different key to unlock the height. Before we start with the height of the polygon, let's take a brief introduction to a polygon.

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What is a Polygon?

A polygon is a generic shape in geometry that contains at least 3 sides and each side is connected. These sides should be straight lines, meaning curve lines are out of the option. There can be more than 3 sides but 3 is the minimum number. There are many types of a polygon such as square, triangle, trapezium, rhombus, and many more. Let's find how to calculate their heights.

How to Find the Height of a Polygon?

The height of a polygon is the length of a perpendicular line drawn from one vertex to the opposite side (or its extension). In simple words, you need to draw a line starting from the base of the polygon to the top-most vertex of the polygon. Don't forget that the line should be at an angle of , meaning an accurate straight line.

 

In the parallelogram, the pencil was placed on the base and with the help of a ruler, it was drawn to the top vertex of the parallelogram. That is the height of a parallelogram. For the case of the triangle, we need to the extent its base otherwise we will end up with a non-straight line or disconnection with the top vertex. That is why you are allowed to extend the base line of a polygon for finding its height.

Orthocenter

 

The orthocenter is the point where all the heights of a triangle intersect. Since the triangle has three corners that means it will have 3 altitudes and all those heights will intersect at a point. Ensure that the heights are drawn perpendicular.

Equilateral Triangle Height

To find the height of an equilateral triangle you will be needing the Pythagorean theorem. By applying the Pythagorean theorem for one half of the equilateral triangle, we obtain:

Example

Calculate the height of an equilateral triangle with a side of .

Isosceles Trapezoid Height

A trapezium is another type of polygon. The height of the trapezium is the distance between both parallel lines. If you construct a straight line from the shortest parallel line's vertex to the longest parallel line, an isosceles triangle will form and you can use the Pythagorean theorem to find the height of the trapezium.

By applying the Pythagorean theorem for one of the triangles, we obtain:

Example

Calculate the height of an isosceles trapezoid whose bases are and , and its side, .

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.