Area of a Triangle

The total space inside the boundary of the triangle is called as the area of the triangle. Area is measured in terms of square unit.

The total space inside the boundary of the triangle is called as the area of the triangle. Area is measured in terms of square unit.

We can find the area of the triangle in several ways.

• Area of the triangle is half the multiplication of base and height of the triangle.

• Area of the triangle can be found using the semi perimeter of triangle with three side values.

• Area of the triangle can be found using the angles of the triangle and two side values.

We can find the area of a triangle in different ways depending upon the value given in the problem.

The area of triangle formulas is, A=1/2(b*h)

Here b is the base of a triangle.

h is the height of a triangle.

One another way to find the area is the Heron's formula. It gives the area in terms of the three sides of the triangle. It is given by the following formula:

Area A = √(s(s - a) (s - b) (s - c))

Here, s is the semi perimeter of the triangle and s = $\frac{(a + b + c)}{2}$.

The area of triangle when two sides and one angle are given is given by the following formula:

Area A= (ab sin C)/2

The above formula says that area of a triangle is the half of the product of two side values and one angle.

Below are some examples based on area of a triangle

Example 1: Find the area of scalene triangle with a base of 15 cm and a height of 4 cm

Area = $\frac{1}{2}$ (b*h)

Substitute the values of base and height. Then we get,

Area = $\frac{1}{2}$ (15*4)

= $\frac{1}{2}$ (60)

= 30 cm²

Example 2: Find the area of a right triangle with a base of 6 meters and a height of 9 meters.

Area = $\frac{1}{2}$ (b * h)

= $\frac{1}{2}$ (6*9)

= $\frac{1}{2}$ (54)

= 27 meter²

Example 3: Find the area of a triangle with two sides 5cm, 8cm and the in between angle is 45 degree.

Area = (ab sin C)/2

= (5*8 sin 45)/2

= (40 *0.85)/2

= (34)/2

= 17 cm²