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In geometry an equilateral triangle is a triangle in which all three sides are equal. To find the area we can first find the height.

Remember Remember The Equilateral Triangle Change Symbol

A 2 a 2 2 h 2.

How to find area of equilateral triangle. In the familiar euclidean geometry an equilateral triangle is also equiangular. Equilateral triangles have sides of equal length with angles of 60. For equilateral triangles h ha hb hc.

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. Consequently each of its three interior angles measure a third of 180 circ which is 60 circ each. Calculate the are using this method.

What is the equilateral triangle. If you have any 1 known you can find the other 4 unknowns. Note how the perpendicular bisector breaks down side a into its half or a 2.

That is all three internal angles are also congruent to each other and are each 60. Now apply the pythagorean theorem to get the height h or the length of the line you see in red. Drag the vertices of the triangle to make a new size triangle.

An equilateral triangle is a triangle with all three sides of equal length. Click show details to verify your answer. To find the height we can draw an altitude to one of the sides in order to split the triangle into two equal 30 60 90 triangles.

Draw the perpendicular bisector of the equilateral triangle as shown below. One of the most interesting and useful properties of an equilateral triangle is that its altitude angle bisector and median from any of its vertices are. So for example if you have an equilateral triangle where each of the sides was 1 then its area would be square root of 3 over 4.

A 2 a 2 4 h 2. Im commentary this tasks examines how to calculate the area of an equilateral triangle using high school geometry further developing 8 g areas of geometric shapes with the same perimeter which performs the same calculation at a level appropriate for middle school. To find the area of an equilateral triangle or a triangle with 3 equal sides all you have to do is to follow these steps.

In this python program we will learn how to find the area of an equilateral triangle. Find the area of triangle abc. Use this formula for the area of an equilateral triangle.

In the figure above click on hide details. The three angles of an equilateral triangle are also of equal measure in euclidean geometry. In this case the upper case a is the area and the lower case a is the length of the sides which again are all equal hence the same letter being used.

A 2 a 2 4 h 2. The surface area of a two dimensional polygon such as a triangle is the total area contained by the sides of the polygon. An equilateral triangle is one in which all three sides are equal in length.

If you had an equilateral triangle where each of the sides were 2 then this would be 2 squared over 4 which is just 1. The altitude shown h is h b or the altitude of b.