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Right Angle Formulas

Right Angle Formulas with solved example: Explore more about the Geometry Formulas with solved examples with solved examples.

Right Angle Formulas with solved examples

The Right-Angle Formulas help to calculate the area and perimeter of right angles and give the fundamental Pythagoras theorem that is used to find the length of the sides of triangles and has several other practical applications.

A Triangle in which one of the interior angles measures 90 degrees is called a right-angled triangle. 

The Right-Angle formulas refer to those formulas that are associated with right-angled triangles and assist in calculating the area, perimeter etc. of the triangle.

The Formulas are as listed below

  • Area = ½ x base x perpendicular

  • Perimeter = Perpendicular + Base + Hypotenuse

  • Pythagoras Theorem

It is a fundamental theorem that shows the relation between different sides of a right-angled triangle, that is, the square of the hypotenuse of the triangle is equal to the sum of the square of the perpendicular and square of the base.

(Hypotenuse)2 = (Perpendicular)2 + (Base)2

Solved Examples

Question 1. If the length of the perpendicular, base and the hypotenuse of a right-angled triangle are given to be 5cm, 6cm and 9 cm respectively, Find:

  1. The Area of the triangle

  2. The Perimeter of the triangle

Solution: To find the Area,

Area = ½ x base x perpendicular

Putting the values,

Area = ½ x 6 x 5 

Or Area = 15 cm2

To find the Perimeter,

Perimeter = sum of all sides 

Or Perimeter = Perpendicular + Base + Hypotenuse

Putting the values,

Perimeter = 5 + 6 + 9 

Or Perimeter = 20 cm

Question 2.  If the length of the perpendicular and base of a right-angled triangle are given to be 5cm and 12 cm respectively, calculate the following:

  1. The length of the hypotenuse

  2. The Area of the triangle

  3. The Perimeter of the triangle

Solution: 

  1. According to the Pythagoras Theorem, 

           (Hypotenuse)2 = (Perpendicular)2 + (Base)2

            Putting the values,

            (Hypotenuse)2 = (5)2 + (12)2

            Or (Hypotenuse)2 = 25 + 144

            Or Hypotenuse = √169 = 13 cm 

  1. Area = ½ x base x perpendicular

            Putting the values,

            Area = ½ x 12 x 5 

            Or Area = 30 cm2

  1. Perimeter = sum of all sides 

            Or Perimeter = Perpendicular + Base + Hypotenuse

            Putting the values,

            Perimeter = 5 + 12 + 13 

            Or Perimeter = 30 cm

faq

Frequently asked questions

Get answers to the most common queries related to the Right Angle Formulas.

Is it possible for a right-angled triangle to have an obtuse angle?

Ans. No, it is not possible for a right-angled triangle to have an obtuse angle because the sum of the interior ang...Read full

Which side of the right-angled triangle is longest?

Ans. The side that is exactly opposite to the 90° vertex, also known as hypotenuse, is the longest side....Read full

Name the three sides of a right-angled triangle.

Ans. The three sides of a right-angled triangle are – Perpendicular, Base and Hypotenuse.