What Are Triangles?

In Geometry, a triangle is a closed two-dimensional figure with 3 sides, 3 angles and 3 vertices. Triangles are considered as a polygon with the least number of sides. In this article, let us discuss what are triangles, its types, properties, and formulas in detail. Learn triangles in detail here.

What are Triangles in Geometry?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered as a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

  1. Scalene Triangle – All the sides are of different measures.
  2. Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
  3. Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

  1. Acute Angle Triangle – All the angles of a triangle is less than 90°
  2. Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°
  3. Right Angle Triangle – One of the angles of a triangle is equal to 90°

Types of Triangles

 

Properties of Triangle

  1. A triangle has three sides, three angles and three vertices.
  2. Sum of all three interior angles of a triangle is 180°.
  3. Sum of the length of two sides of the triangle is greater than its third side.
  4. The area of a triangle is the half  the product of the base and the height
  5. The perimeter of a triangle is the sum of all the three sides of a triangle.

Area of Triangle

One of the properties of a triangle is its area, which is the region covered by the three-sided polygon in a plane. The formula for any triangle’s area is given by;

Area of a Triangle = ½ × Base × Height

One more formula has been introduced by a Mathematician, which is known as Heron’s Formula. This formula is used when the sides of the triangles are known to us. It is given by;

Area of Triangle-Heron's Formula

Where ‘s’ is the semi-perimeter of the triangle and given by;

s = (a+b+c)/2

Where a, b and c are the measure of the three sides of the triangle.

Perimeter of Triangle

The perimeter of a triangle is the length covered by the sides of the triangle in a plane. The formula of the perimeter is given by;

P = a + b + c

 

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Frequently Asked Questions on What Are Triangles

Find the perimeter of a triangle, whose sides are 3 cm, 4 cm and 6 cm.

Given, sides of the triangle are 3 cm, 4 cm and 6 cm.

Let a = 3 cm, b = 4 cm and c = 6 cm

By the perimeter formula, we know;

P = a+b+c

P = 3+4+6 = 13 cm

Find the perimeter of an isosceles triangle whose base is 9 cm and sides are equal to 12 cm.

For an isosceles triangle, two sides are equal to each other.

Therefore, the perimeter of an isosceles triangle, P = 2xa + b

P = 2 x 12 + 9

P = 24 + 9

P = 33 cm