Area is two dimensional like a mat while triangle is a three sided polygon. There are different methods to find the area of the triangle.

1. The most commonly used and known method is 'Half base times height' method.
2. Heron's formula - Length of all three sides should be known.
3. Side angle side method where two sides and one angle is known.

## Formula for Area of a Triangle

Given below are the formula's to find the area of a triangle using different methods.

'Half base times height' method.

Area = $\frac {b \times h}{2}$
where b is the length of the base and h is corresponding height.

Heron's formula
Let a, b, c be the lengths of the sides of a triangle then the area is
A = $\sqrt{s(s-a)(s-b)(s-c)}$

s is half the perimeter = $\frac{a+b+c}{2}$

Side angle side (SAS) formula
Let a, b be the known sides and C is the known included angle. The formula is
A = $\frac{a \times b \times Sin C}{2}$

## How To Calculate the Area of a Triangle

### Solved Examples

Question 1: If the two sides of a triangle have measures of  6 and 14 with the measure of the included angle known to be 60$^{0}$ then what is the area of the triangle?
Solution:

We use Side angle side formula and is given by
A = $\frac{a \times b \ Sin C}{2}$

A = $\frac{6 \times 14 \ Sin 60 ^{0}}{2}$

A = $\frac{(6 \times 14) \ 0.866}{2}$

A = 36.37 sq .units
Therefore the area of the triangle is 36.37 sq .units

Question 2: Find the area of the triangle whose base is 6 cm and height is 15cm.
Solution:

The formula for half base times height is given by
A = $\frac{b\times h} {2}$
Plug in the given values
A = $\frac{15\times 6} {2}$

A = 45 cm$^{2}$.

## Surface Area of a Triangle

Surface area can be found only for three dimensional figures not for two dimensional figures. The formula for perimeter of a triangle is

P = a + b + c
where a, b, c are the lengths.

Perimeter is a path having a two-dimensional shape and the length of the boundary can be found by adding all the three sides.

## Area of a Triangle Examples

### Solved Examples

Question 1: Find the area of a triangle whose sides are 5 m, 6 m and 7 m respectively.
Solution:

Let a = 5m, b = 6m and c = 7m
We use heron's formula to find the area of a triangle and is given as
A = $\sqrt{s(s-a)(s-b)(s-c)}$     ----> 1

First we find the perimeter

s= $\frac{5 + 6 + 7}{2}$

s = 9

Substitute the value of s in equation (1)

A = $\sqrt{9(9 - 5)(9 - 6 )(9 - 7)}$

A = 14.69 m$^{2}$

Therefore the area of the triangle is   A = 14.69 m$^{2}$.

Question 2: Find the area of the triangle whose base is 12 cm and height is 14cm  respectively.
Solution:

The formula for half base times height is given by
A = $\frac{b \times h} {2}$

Plug in the given values

A = $\frac{12 \times14} {2}$

A = 84 cm$^{2}$.