Area of a Triangle – How to calculate area and perimeter of triangle
In this article, we will see the different ways to calculate the area and perimeter of a triangle along with other associated concepts. A geometrical shape or a polygon that has three sides and three vertices are referred to as a triangle. There are several sister topics that are associated with a triangle, such as Pythagoras theorem, trigonometry, algebra, etc. Thus, students must have a clear understanding of the basic concepts such as the area of triangle, its perimeter, and properties.
Area of a Triangle
The area of a triangle can be defined as the region or the space that is enclosed by all three sides of a triangle. There are three basic methods to calculate the area of any triangle.
We will first take a look at Heron’s formula to find the area of a triangle.
Let us suppose that we have a triangle, and the side lengths are given by m, n, l then according to this formula
Area of a triangle = s (s-m)(s-n)(s-l)
where, s stands for the semi – perimeter of the triangle and is given by
s = ( m + n + l) / 2
This formula is used when all three sides of a triangle are known.
However, there are several instances where we might not know all three sides. In such a case, we can calculate the area by dropping a perpendicular from one vertice, which gives the height, to the opposite side, which gives the base. The formula is given by
Area of a triangle = ½ (base)(height)
There are cases where two sides of a triangle and the included angle are known. In that situation, you have to apply trigonometric formulas to find the area of a triangle. If we have a triangle PQR with side lengths given by p, q, r, and angles P, Q, R, then you can find the area of the triangle by either one of the following formulas depending upon what is known.
- A(PQR)= ½ qr sin P
- A(PQR)= ½ rp sin Q
- A(PQR)=½ pq sin R
The Perimeter of a Triangle
The perimeter of any polygon is given by the sum of lengths of all its sides. Thus, the perimeter of a triangle is the total distance covered by the three sides or boundaries of that triangle. In other words, the perimeter of a triangle is given by the sum of all its three sides. Suppose we have a triangle PQR with side lengths PQ, QR, PR. Then the formula for the perimeter is given as follows:
The perimeter of a triangle = addition of the three sides = PQ + QR + PR
Triangles can prove to be a confusing topic; hence, it is best if you took help from an external institution such as Cuemath. Cuemath is a fantastic online educational platform that provides a very good quality of education to children. The certified tutors use several resources such as worksheets, puzzles, apps, visual simulations, etc., to deliver an impactful lecture. Students are given the flexibility to maintain their own pace of learning. Thus, this enables them to instill a strong foundational understanding of the topic being taught. Good grades inevitably follow.
Classification of Triangles
Based on Sides
- Equilateral Triangle – all sides are equal.
- Isosceles Triangle – only two sides are equal.
- Scalene Triangle – all the sides are unequal.
Based on Angles
- Acute Triangle – all the angles are less than 90 degrees.
- Right Triangle – only one angle measures 90 degrees.
- Obtuse Triangle – only one angle greater than 90 degrees.
Hopefully, this article helps you to get a better understanding of triangles and how to study them!