A triangle is a shape with three straight lines that connect to make three corners. If all sides of a triangle are the same size, we call it an equilateral triangle. In an equilateral triangle, all three corners have the same angle, which is 60 degrees. When we discuss an equilateral triangle, we refer to characteristics like its properties, how long its boundaries are; and how much space it covers. Now, let’s learn about the ways to figure out how much area an equilateral triangle has.
1. Heron’s Formula
This equation helps us calculate the area of a triangle if we have the measurements for all three sides. First, we find the perimeter of the triangle, which is the total length of all the sides, and then we halve that number. Now we can use this new number to work out how much space the triangle has inside. Let’s say we have a triangle and its sides are j, t, and l.
Semi perimeter, s = (j + t + l) / 2
Area of the triangle = √[s (s – j) (s – t) (s – l)]
So in a triangle where all the sides are the same length, we can call that length d. Now, if we take the formula we were discussing earlier, we slot in d for the side lengths. Once we do that, instantly, we’ll land on the area.
Semi perimeter of equilateral triangle = 3d/2.
Area of equilateral triangle = √3d2/4.
2. Base Height Formula
When we make a line go straight down from one corner of the triangle to the edge right opposite, this line is the triangle’s height, and the edge it lands on is the base; to calculate the triangle’s area, we follow this formula.
Area of a triangle = ½ × (base) × (height)
In a triangle where each side is the same length, you can work out its height using the Pythagorean theorem. Because the height divides the bottom side evenly in half, that formula helps us find how tall it is. Say every side of the triangle measures d, this is the way we do the math.
Height = √3d/2
Area = ½ (d)(√3 d/2) = √3d2/4
What is an Isosceles Triangle?
A triangle in which two sides are of equal length is known as an isosceles triangle. This also implies that the two angles opposite to the equal sides are equal.
The area of isosceles triangle formula can be given by two methods similar to the ones discussed above.
1. Heron’s Formula
Let the length of equal sides of the triangle be given by m, and the third side measures n. Then by substituting these values in the heron’s formula, we get
Semi perimeter s = (m + m + n)/2
Area of an isosceles triangle = n/2 × √[m2 – n2/4]
2. Base Height Formula
We can find the height of the triangle by the Pythagoras theorem and use this value to find the area.
Height = m
Area of an isosceles triangle = ½ m2.
Conclusion
There are different ways to figure out the size of triangles, like using math formulas based on triangles’ angles. Some students might find it tricky to measure the space inside a particular triangle by changing its shape or form — that’s why they could benefit from signing up for an online math program like Cuemath. At Cuemath, certified teachers use all kinds of techniques to make learning math seem less scary. They give children items like workbooks, activity sheets, and math games to keep things interesting. What’s really important is how they focus a lot on making sure all the basic math skills are solid, so a student can tackle simple or tough problems with no sweat. I hope this piece of writing clears up things about triangles for you, and I wish you the best in your math journey!
