## Area of a Triangle

Triangle is one of the basic polygons in Geometry. Triangle is a polygon or a shape which has 3 sides and 3 vertices. Triangles are classified into 3 types depending on the lengths of the sides. They are Equilateral Triangle, Scalene Triangle, and Isosceles Triangle.

#### Area of Triangle:

To find the area of the triangle there are different ways to find it. Through this article we are providing all the methods which are available to find the area of the Triangle.

#### How to Find the Area of a Triangle When we Know its Height & Base?

If we know the height and base of the triangle then by using the following formula we can find the area of the triangle.

**Area of the Triangle = ½ bh**

#### Example:

Find the area of a triangle whose height is 12 & base is 20.

Solution:

Height of the Triangle – 10

Base of the Triangle – 20

Area = ½ bh => ( Area = ½ * b * h)

Now substitute the values into the formula

Area = ½ * 20 * 10

Area = 200/2

Area = 100

#### How to Find the Area of Triangle when we the lengths of all three side?

When we know the lengths of the triangle then we can find the area of the triangle by using the Heron’s Formula.

#### Finding the Area of the Triangle by Using Heron’s Formula:

Heron’s formula includes 2 steps they are first step to find the s, where s is half of the triangle’s perimeter of which we are going to find the area and the second step is finding the area.

**Step1: **Calculate
the half of the Perimeter of the Triangle

**S = a+ b+ c/2**

**Step2**: Area of the Triangle

**A = √ ** **(s-a) (s-b) (s-c)**

#### What is the Area of a Equilateral Triangle whose side is 5

**Solution:**

**Step1: **

S=a+ b+ c/2

S= 5+5+5/2

**S= 7.5 ** (Where S- half of the Perimeter of the
Triangle)

**A = √ ** **(s-a) (s-b) (s-c)**

**A = √ **7.5(7.5-5) (7.5-5) (7.5-5)

**A = √ **7.5 x 2.5 x 2.5 x 2.5

A= 117.1875

**A = 10.825**

#### How find the Area of Triangle when we know 1 angle and two sides?

By using the following formula we can find the area of the triangle when we know the 2 sides and one angle.

**Area = ½ ab Sin C**

**Area = ½ bc Sin A**

**Area = ½ ca Sin B**

#### Find the Area of the Triangle of Angle C = 25, and Side a=8, b=10

Here in this problem we know one angle of the triangle i.e. C = 25, and the two sides of the triangle a & b where a= 8 and b = 10. In this case we can use the first formula

**Solution:**

Area of the Triangle = ½ ab Sin C

Substitute the a, b, c values in the above formula

Area = ½ 8 x 10 Sin 25

Area = ½ x 80 x 0.4226

Area = 40 x 0.4226

**Area = 16.904**

#### Find the Area of the Triangle of Angle A = 25, and Side b=6, c=10

Here in this problem we know one angle of the triangle i.e. A = 25, and the two sides of the triangle b & c where b= 6 and c = 10. In this case we can use the first formula

**Solution:**

Area of the Triangle = ½ bc Sin A

Substitute the a, b, c values in the above formula

Area = ½ x 6 x 10 Sin 25

Area = ½ x 60 x 0.4226

Area = 30 x 0.4226

**Area = 12.67854**

#### Find the Area of the Triangle of Angle B = 25, and Side a=7, a=10

Here in this problem we know one angle of the triangle i.e. C = 25, and the two sides of the triangle a & b where a= 7 and b = 10. In this case we can use the first formula

**Solution:**

Area of the Triangle = ½ ca Sin B

Substitute the a, b, c values in the above formula

Area = ½ 7 x 10 Sin 25

Area = ½ x 70 x 0.4226

Area = 35 x 0.4226

**Area = 14.79163**

#### Type of Triangles:

Depending on the lengths of the sides Triangles can be classified into 3 types. They are

- Equilateral Triangle
- Scalene Triangle
- Isosceles Triangle

#### Equilateral Triangle:

Equilateral triangle is one type of triangle in which all the 3 angles are measuring 60. i.e. all the three sides in the equilateral triangle are equal.

#### Isosceles Triangle:

Isosceles triangle is the second type of triangle in which two sides are having equal lengths.

#### Scalene Triangle:

Scalene triangle is the third type of triangle in which all the sides have different lengths.