How to Find the Area of Isosceles and Scalene Triangle?

Isosceles and scalene triangles are a type of triangle. They can be classified based on their angles, properties, and formulas for their area. In this article, we will discuss what these triangles are and how to calculate their formulas.

What is an Isosceles Triangle?

Any triangle with two equal and similar sides is called an isosceles triangle. In addition, the two angles on the opposite sides of the two equal sides are also equal. To put it another way, “an isosceles triangle is a triangle with two congruent sides.” If the sides AB and AC of a triangle ABC are equal, then ABC is an isosceles triangle with B = C. The isosceles triangle is defined and expressed by the theorem that if the two sides of a triangle are congruent, then the angle opposite them is also congruent.

Isosceles Triangle Area:

The region occupied by an isosceles triangle in two-dimensional space is known as its area. In general, the base and height of an isosceles triangle are half the product of the base and height. The region of an isosceles triangle can be calculated using the following formula: A = 12 b h Square units are the area of isosceles triangle, where b is the triangle’s base while h is its triangle’s height.

Isosceles Triangle Properties

  1. In any given triangle the two sides are equal, the unequal side is named as the base of the triangle.
  2. The angles opposite to the two similar sides of the triangle are always equal.
  3. The altitude or the height of an isosceles triangle is measured from the base to the vertex of the same given triangle.
  4. A right isosceles triangle always will have a third angle of 90 degrees.

Commonly, the isosceles triangle is classified into three different kinds namely:

  • Isosceles acute triangle
  • Isosceles right triangle
  • Isosceles obtuse triangle

What is a Scalene Triangle?

A scalene triangle is one in which each of the three sides has a different length and each of the three angles has a different measurement. The number of all interior angles, on the other hand, is always 180 degrees. As a result, it satisfies the triangle’s angle sum property condition.

Classification of Triangles

According to the sides and the interior angles of a triangle, there are three various types of triangles. Due to the interior angles of the triangle, they can be divided into three types, namely:

  • Acute Angle Triangle
  • Right Angle Triangle
  • Obtuse Angle Triangle

Properties

Some of the vital properties of the scalene triangle are as stated:

  • They have no equal sides.
  • They have no equal angles.
  • They have no line of symmetry.
  • They have no point symmetry.
  • The angles inside the same respective triangle can be acute, obtuse, or right-angled in nature.
  • If all the angles of the triangle are less than 90 degrees that is an acute triangle, then the center of the circumscribing circle will lie inside the sides of a triangle.
  • In a scalene obtuse triangle, the circumcenter will lie outside the side of the triangle.
  • A scalene triangle can either be an obtuse-angled, acute-angled, or right-angled triangle depending on its degree of angles.

How to Obtain the Area of a Scalene Triangle?

The formula for finding the area of scalene triangle is given below:

Area of a scalene triangle = (1/2) x b x h square units

Where,

“b” symbolizes the base of the triangle

“h” symbolizes the height of the triangle

If the sides of any of the given triangles are provided, then one can apply Heron’s formula.

Area of the triangle = A=√s(s−a)(s−b)(s−c) square units

Where,

“s” symbolizes the semi perimeter of a triangle, which can be obtained by using the formula

s = (a+b+c)/2

Here, a, b, and c expresses the sides of the triangle.