The equilateral triangle is being defined as a triangle that has equal sides. The area of the equilateral triangle is the measurement of the region which is covered by the boundaries of the equilateral triangle. Let us first recall, what is an equilateral triangle? Well, these triangles have equal sides with 60 degrees as the internal angle measurement. To calculate the area of equilateral triangle we need to know the length of the side.
The formula for the area of the equilateral triangle is A = (√3/4) a2. In this case, ‘a’ represents the length of the sides.
The area of the equilateral triangle can be derived using three methods. They are as follows:
- Using the basic formula of the triangle.
- Using the construction of a rectangle.
- Also, you can use trigonometry
We need to measure the sides of the equilateral triangle which is represented by the ‘a’ unit. After which you need to draw a perpendicular which will act as the height of the equilateral triangle represented by ‘h’.
Now, we know the formula of the area of the triangle, which is ½ × base × height
Then you need to apply the Pythagoras Theorem formula and calculate the area of the equilateral triangle from the equation. The derivation’s final answer will come as – A = ½ × a × ½(√3a)
Or, this can be represented as – Area of Equilateral Triangle = ¼(√3a2)
By now, we know the features of the equilateral triangle, so to sum it up we need to analyze the properties of the equilateral triangle.
Thus, the properties of the equilateral triangle are as follows:
- This is a triangle where all three sides are equal in measurement.
- The angles of this triangle are also equal, that is they are equiangular as well.
- The angles measure 60 degrees each.
- This is a type of polygon with only three sides.
How Would You Define the Area of a Triangle?
After learning the area of the equilateral triangle, it will be better to discuss the basics as well, so in this context, we will now head on to discussing the area of a triangle.
As known, the area of the triangle is the measurement of the covered region encompassed between the three sides. The triangle which has its sides and vertices summing up to three consists of an enclosed region, which we need to take out the measurement. Thus, the area of the triangle is the total region that is covered by the specific triangle.
Generally, to find out the formula of the area of triangle, we need to understand the concept. The formula basically, comes to form the derivation of the equation of the Pythagoras Theorem.
So, the Formula for the Rae of the Triangle is –
A = ½ (b × h) square units
In this equation, b and h is the base and height of the triangle respectively.
After learning what is a triangle, the properties of the triangle, derivation of the formula will turn out to be a lot easier. Next, the students will know about the area of the triangle and thereby they can apply the formula into sums and estimate the final answers as the area of the triangle.
As we come to the end of this discussion, the students have gained knowledge about the equilateral triangle, the formula of the area of the equilateral triangle, next we went to the basic understanding of learning the area of the triangle. Also, by practicing more such sums based on the area formula we will know the concept better eventually.
Students aspiring to know more about such mathematical concepts are welcome to visit Cuemath for an engrossed mathematical discussion.