# Triangle Formulas

A triangle formula is used to calculate the perimeter and area of a three-sided polygon which is also known as trigon. Let us learn the triangle formulas in detail.

## What Are Triangle Formulas?

The two important triangle formulas are the area of a triangle formula and the perimeter of a triangle formula. Further, the triangle formulas are applicable to different types of triangles.

### Area of Triangle Formula

The area of the triangle is equal to half of the product of the base and height of the triangle, it is given as,

**Area of triangle, A = [(½) base × height] square units.**

There are two important triangle formulas related to the area of a triangle, i.e., the Herons formula and the Pythagoras theorem.

The area of a triangle using Heron's Formula is given as,

Area of triangle ABC = \(\sqrt{s(s-a)(s-b)(s-c)}\),

where s is the semi-perimeter = Perimeter/2 = (a + b + c)/2

Pythagoras theorem is used to find the side of the right-angled triangle which is mathematically expressed as, h^{2} = p^{2} + b^{2}. Here, 'h' is the hypotenuse (longest side of a right triangle), p is the perpendicular side, and b is the Base.

In the case of an equilateral triangle, the equilateral triangle formula for area is, A = (√3/4)a^{2 }square units, where a is the side of the triangle.

In the case of an isosceles triangle, the isosceles triangle formula for area is, A = 1/2 × Base × Height square units, where, height = \(\sqrt{\text{a}^2 - \dfrac{b^2}{4}}\). (Here 'a' is the equal side, and 'b' is the base of the isosceles triangle.)

### Perimeter of Triangle Formula

The perimeter of the triangle is equal to the sum of all the sides of the triangle, it is given as

**General perimeter of a triangle formula, P = (a + b + c) units.**

The equilateral triangle formula for perimeter is (a +a + a) = 3 a units. Here 'a' is a side of an equilateral triangle. (Note: in equilateral triangle all three sides are equal)

The isosceles triangle formula for perimeter is (s + s + b) = (2s + b) units, here s is a measurement of two equal sides, and b is the base of an isosceles triangle.

## Examples on Triangle Formulas

**Example 1: **Find the area of a triangle whose base is 40 units and its height is 25 units.

Solution:

To find: The area of a triangle

The base of a triangle = 40 units (given)

Height of triangle = 25 units (given)

Using triangle formulas,

Area of triangle, A = [(½) base × height] square units

= [(½) 40 × 25] square units

= 500 square units

**Answer: The area of the triangle is 500 square units.**

**Example 2: **A triangle has sides a = 5 units, b = 10 units, and c = 6 units. What is the perimeter of this triangle?

Solution:

To find: The perimeter of a triangle

Three sides of a triangle = 5, 10, 6. (Given)

Using triangle formulas,

Perimeter of a triangle, p = (a + b + c) units.

= ( 5+10+6) units.

= 21 units

**Answer: The perimeter of a triangle is 21 units.**

**Example 3:** If the lengths of the sides of a triangle are 4 in, 7 in, and 9 in, calculate its area using Heron's formula.

Solution:

To find: Area of the triangle

Given that, Side a = 4 in, Side b = 7 in, Side c = 9 in

Using triangle formula (Heron's Formula),

A = √(s(s-a)(s-b)(s-c))

As, s = (a+b+c)/2

s = (4+7+9)/2

s = 20/2 = 10 inches

Substituting the values in the Heron's formula,

A = √(10(10-4)(10-7)(10-9))

⇒ A =√(10(6)(3)(1))

⇒ A = √(180) = 13.416 in^{2}

**∴ The area of the triangle is 13.416 in ^{2}.**

## FAQs on Triangle Formulas

### What Are Equilateral Triangle Formulas?

The equilateral triangle formula for area is, A = (√3/4)a^{2} , here a is the side of a triangle

The equilateral triangle formula for perimeter is (a +a + a) = 3 a. Here a denotes side of an equilateral triangle of equal measurement.

### What Are Isosceles Triangle Formulas?

The isosceles triangle formula for area is, Area = 1/2 × Base × Height (units^{2}).

The isosceles triangle formula for perimeter is (2s + b), here 2s is a measurement of two equal sides and b denotes the base of an isosceles triangle.

### What are the Two Basic Triangle Formulas?

The two basic triangle formulas are the area of a triangle and the perimeter of a triangle formula. These triangle formulas can be mathematically expressed as;

- Area of triangle, A = [(½) base × height] square units.
- Perimeter of a triangle, P = (a + b + c) units

### What Are Scalene Triangle Formulas?

The scalene triangle formula for area is, Area = 1/2 × Base × Height (units^{2}).

The scalene triangle formula for perimeter is (a + b + c), where a, b, and c denote the unequal sides of a scalene triangle.

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