Perimeter and Area of Triangle

Scalene Triangle

Scalene Triangle

A triangle whose three sides have different lengths is called a scalene triangle. That is, AB ≠ BC ≠ CA.

If any side of a triangle is taken as the base, the perpendicular drawn from the opposite vertex to that side or to its extension is called the height or altitude of the triangle. In the figure above, h represents the height of acute-angled, obtuse-angled and right-angled triangles.

🔹 Area of a triangle = × base × height = × AB × h

Area of a Scalene Triangle

If the three sides of triangle ABC are a, b, c respectively:

🔹 Perimeter of the triangle = (a + b + c) units

🔹 Semi-perimeter units

🔹 Area of the triangle = sq. units

If the areas represented by the two formulas above are equal, we can write:

🔹 =

Therefore, if the values of a, b, and c are known, the value of h can be calculated.

Equilateral Triangle

Area of an Equilateral Triangle

A triangle whose three sides are equal is called an equilateral triangle.

If AB = BC = CA = a, then:

🔹 Perimeter of an equilateral triangle = 3a units

🔹 Height of an equilateral triangle = units

🔹 Area of an equilateral triangle = sq. units

Equilateral Triangle

Let O be any point inside equilateral triangle ABC. From O, draw perpendiculars of lengths p, q, and r to the sides AB, BC, and CA respectively, and join OA, OB, OC. Also draw CD perpendicular to AB from vertex C.

If CD = h and AB = BC = CA = a, then:

🔹 △AOC + △COB + △AOB = △ABC

or,

or, p + q + r = h

Isosceles Triangle

A triangle in which any two sides are equal is called an isosceles triangle.

Isosceles Triangle

That is, AB = AC ≠ BC.

If the equal sides are a and the base is b:

🔹 Perimeter of an isosceles triangle = 2a + b units

🔹 Height of an isosceles triangle = units

🔹 Area of an isosceles triangle = sq. units