**What is a triangle?**The plane closed figure, with three sides and three angles is called as a triangle.

**Types of Triangles (Based on the sides)**

- Equilateral triangle
- Isosceles triangle
- Scalene triangle

**Types of Triangles (Based on the sides)**

- Acute angled triangle
- Obtuse angled triangle
- Right angled triangle

**AREA OF TRIANGLE**

**Area of triangle or right angle triangle**= ½*base*height

**Area of equilateral triangle** = √3a2/4

**Area of isosceles triangle**= (1/4) × b × √ (4a2 – b2)

**AREA OF TRIANGLE BY HERON’S FORMULA**

Area = √[s(s – a)(s – b)(s – c)]

Where s= (a+b+c)/2

**Example**– A triangle PQR has sides 4 cm, 13 cm and 15 cm. Find the area of the triangle.

Semi perimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16 cm

By heron’s formula,

A = √[s(s-a)(s-b)(s-c)]

Hence, A = √[16(16-4)(16-13)(16-15)] = √(16 x 12 x 3 x 1) = √576 = 24 sq.cm

**Example**–**The sides of triangle are a, a, a units**

s=(a+ a+ a)/2=3a/2

Using Heron’s formula

Area of equilateral triangle is

**HERON’S FORMULA FOR QUADRILATERAL**Let ABCD he a quadrilateral to find the area of a quadrilateral we need to divide the quadrilateral in triangular parts

Here AB||CD and AC & BD are the diagonals.

AC divides the quad ABCD into two triangles ADC and ABC.

Now we have two triangles here.

Area of quad ABCD = Area of ∆ADC + Area of ∆ABC (Calculate area of triangles by Heron’s formula)