**Right Triangle Formula**

A triangle is a closed figure with 3 sides, 3 angles and 3 vertices and for right triangles formulas, the properties have to be more specific. If any one of the angles of a triangle is a right angle measuring 90°, the triangle is called a right angled triangle or simply, a right triangle.

A right triangle formula would help you solve variety calculations related to the perimeter area, etc of the right triangle.

**What are the Right Triangles Formulas?**

A right-angled triangle is one which has one of its interior angles measuring 90 degrees. Right angled triangle formulas are used to calculate the perimeter, area, height, etc of a right triangle using its three sides.

Pythagoras theorem: (Hypotenuse)² =(Altitude)² + (Base)²

Area = 1//2 × base altitude

Perimeter = Hypotenuse + Base + Altitude.

**Right Angled Triangle Formula:**

Different formulas associated with the right triangle are:

- Pythagoras theorem formula definition shows relations among the three sides of a right triangle. The square of the hypotenuse is equal to the sum of squares of the other two sides.

(Hypotenuse)² =(perpendicular)² +(Base)²

- Area of a right triangle formula is given as

Area =1/2 × Base height = ½ × b h

Where height, h is equal to the length of the perpendicular side of the triangle.

- The perimeter of a right triangle formula is given as

Perimeter = a + b + c

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

**Example:**

**Question: **The length of the base and perpendicular of a right-angled triangle is 6 in and 3 in respectively. Find the length of its hypotenuse, the perimeter of the triangle and area of the triangle.

**Solution:**

Length of base =6 in, length of perpendicular = 8 in

1. Using Pythagoras’ theorem,

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

(Hypotenuse)² = 6² +8² = 100

Hypotenuse = √100 = 10 in

2. Using the perimeter of a right triangle formula,

Perimeter = 6+8+10= 24in

3. Using the area of triangle formula

Area= (1/2) b ×h

(1/2) ×6 × 8 = 24in².